Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. In this video, we restrict the domains of the sine and cosine functions so that the graphs satisfy the horizontal line tests and therefore become graphs of invertible functions and use reflection in the line y equals x to visualize the inverse sine function. For multiplication, it's division. The inverse trigonometric functions. If your calculator is in radian mode, then you should get 0.93 radians to two decimal place. Arcsecant. These are called arcussine, arcuscosine, arcustangent, arcuscotangent, arcussecant, arcuscosecant, and are denoted, respectively, by Arcsinx, Arccosx, Arctanx, Arccotanx, Arcsecx, Arc\cosecx. The inverse trigonometric functions are the inverse functions of the trigonometric functions. Inverse circular functions. Inverse Circular Functions. To make each inverse circular function single valued we define principal value as follows. Maybe you conjure up in your mind an image of a 30-degree right angled triangle with side length one-half, sine of 60 degrees or pi on 3 radians is root 3 on 2. This checks out because 53 multiplied by the conversion factor power on a 180 is approximately 0.93 radians. If not, have a look on Inverse trigonometric function formula. So the range is the interval from negative 1 to 1 including both endpoints. represent angles or real numbers and their sine is x, cosine is x and tangent is x , given that the answers are numerically smallest available. Thus, for the above domain and range the functions sin-1x, cos-1x and tan-1x becomes the functions of x. Plus, you get useful links. Our function is mapping 0 to 4. Circular functions The circle below is drawn in a coordinate system where the circle's center is at the origin and has a radius of 1. Sequence and Series and Mathematical Induction. So, we focused on this very nice space of the tan curve which satisfies the horizontal line test. Or, 3tan-1 (2 – 3√3) – tan-11x1x = tan-113.13. For example, sinusoidal degrees or sine upon 6 radians is a half. Taking phi away gives us theta equals this very nice explicit expression involving fractions and inverse tan. Arccosine. Summary of Inverse Circular Functions Interval Ran e Quadrants of the Unit Circle Inverse Function Domain sin cos tan cot sec csc x x x X x x . Again, just think of tan as taking angles to numbers and inverse tan is bringing numbers back to angles. In other words, the inverse cosine is denoted as \({\cos ^{ - 1}}\left( x \right)\). Forums. inverse y = x x2 − 6x + 8 inverse f (x) = √x + 3 inverse f (x) = cos (2x + 5) inverse f (x) = sin (3x) Arccosecant. Here's an application. Range of usual principal value There are six inverse trigonometric functions. The domain of f is the range of f –1, and the range of f is the domain of f –1. There are particularly six inverse trig functions for each trigonometric ratio. Aug 2008 220 1. Because over here, on this line, let's take an easy example. We can graph the relationship between x and tan x for these values of x and it looks like this. functions respectively. [3tan-1x = tan-1(3x−x31−3x2)(3x−x31−3x2)], Or, tan-1{(3(2−3√)−(2−3√)2)1−3(2−3√)2}{(3(2−3)−(2−3)2)1−3(2−3)2} – tan-11313= tan-11x1x. The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. This fragment has a very pleasant rotational symmetry about the origin. Because tan x is sine x on cos x, the periodic behaviors of sine and cosine mean that this picture reproduces itself at infinite on both to the right and to the left with infinitely many vertical asymptotes, which in fact occur at odd multiples of plus or minus pi on 2. The principal inverses are listed in the following table. In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions ) are the inverse functions of the trigonometric functions (with suitably restricted domains). The module covers quadratic, cubic and general power and polynomial functions; exponential and logarithmic functions; and trigonometric functions related to the mathematics of periodic behaviour. The inverse sine function is defined by y = sin-1x. This chapter’s six functions – the inverse cosine function arccos(x), the inverse sine function arcsin(x), the inverse secant function arcsec(x), the inverse cosecant function arccsc(x), the inverse tangent function arctan(x) and the inverse cotangent function arccot(x) – are known collectively as the inverse circular functions or the inverse trigonometric functions. An inverse function goes the other way! This is an amazing course. Now, L.H.S.= 1212(2sin2A + 2sin2B) + sin2C. We can evaluate this using a calculator to get approximately 0.17 radians, which is about 9.8 degrees. There sine x and cos x are defined for all real numbers x interpreted as angles that wind around the unit circle. You can not skip it while learning mathematics. Students can read from the Inverse Trigonometric Functions Formulas List Class 12 and memorise it for solving numerical. Properties of inverse trigonometric functions (5) Principal values for inverse circular functions: (6) Conversion property: We have similar behavior in the negative direction if we move in the fourth quadrant from zero towards negative pi on 2. One of the more common notations for inverse trig functions can be very confusing. Remember, inversion interchanges domain and range, so the domain of inverse tan is the range of tan which is the entire real number line, and the range as in this tan is the domain of our fragment of tan which is the interval from negative pi on 2 to pi on 2 but not including the end points. We also sketch the graph of the tan function and repeat this process to describe the inverse tan function. The adjacent side is the ground but we don't need to know what its length is to solve the problem. Assuming the string is approximately straight, we want to estimate the angle of elevation which we call theta. Domain = {x:-∞ < x < ∞} and range = {y: π2π2 ≤ y ≤ π2π2}. We can reflect in the line y equals x to invert the function, producing the graph of y equals inverse tan of x. We showed how to create new functions by means of composition and inversion both geometrically by reflecting in the line y equals x and by algebraic manipulation. Domain and Range of inverse trigonometric functions. Just now we discussed the inverse sine and inverse tangent functions and briefly illustrated how that can be used to interpret numerical information in terms of angles. The inverse trigonometric functions are the inverse functions of the trigonometric functions. There's another right angle triangle, with angle phi plus theta with opposite side length 46 plus 46 equals 92 meters and adjacent side length again 250 meters. This module introduces the notion of a function which captures precisely ways in which different quantities or measurements are linked together. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. Summing to sine of minus 1 gets you back to minus pi on 2. The roles of input and output have been interchanged so the labels plus and minus pi on 2 now become points on the vertical axis and the labels plus or minus 1 now become points on the horizontal axis, and we have the graph of y equals inverse sine of x. Students taking Introduction to Calculus will: For example, tan of 45 degrees or pi of 4 radians is 1. So, I'm doing this because as phi equal to inverse tan of that fraction. The inverse function, if you take f inverse of 4, f inverse of 4 is equal to 0. = 1 – sinC [2sinA−B+A+B2.sinA+B−A+B2][2sin⁡A−B+A+B2.sin⁡A+B−A+B2]. This solves our original problem. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions. J. Joker37. First, regardless of how you are used to dealing with exponentiation we tend to denote an inverse trig function with an “exponent” of “-1”. Though we haven't been asked to find it, let us denote the angle subtended by the pedestal by another angle called phi. Then … Made calculus very approachable connecting topics, illustrating applications, and his enthusiasm (which is contagious). To simulate the reflection, we can take a transparency with this fragment and flip it over. Just think of the sine function as taking angles to numbers and inverse sine function is bringing numbers back to angles. Arc tan(−13√)(−13) = tan-1(−13√)(−13) = -tan-1(13√)(13) = −π6−π6. Construction Engineering and Management Certificate, Machine Learning for Analytics Certificate, Innovation Management & Entrepreneurship Certificate, Sustainabaility and Development Certificate, Spatial Data Analysis and Visualization Certificate, Master's of Innovation & Entrepreneurship. We know about inverse functions, and we know about trigonometric functions, so it's time to learn about inverse trigonometric functions! So, the horizontal line test fails spectacularly for both graphs. Inverse Circular Functions takes more questions from Chapter 18 of Loney's Plane Trigonometry. Our function, when you take 0-- so f of 0 is equal to 4. Inverse trigonometric functions are widely used in engineering, navigation, physics, … We can severely restrict their domains to that we get a fragment of each graph that passes the horizontal line test. In the diagram, you can see a right angle triangle with angle theta opposite side then 40 meters and hypotenuse represented by the string of length 50 meters. To view this video please enable JavaScript, and consider upgrading to a web browser that Trigonometry. Wish he'd do follow-up courses for more advanced mathematics. Or the inverse function is mapping us from 4 to 0. This is in fact the last video for module two. We've talked about linear functions whose graphs of lines and quadratic functions whose graphs of parabolas, and discussed techniques involving completing the square and the quadratic formula. Since none of the six trigonometric functions are one-to-one, they are restricted in order to have inverse functions. Because we moved from points on the unit circle across the vertical axis of sine x and down or up to the horizontal axis of cos x, the values are trapped between plus and minus 1. Enter the inverse tangent of the And for trigonometric functions, it's the inverse trigonometric functions. To solve this, observe that sine theta is the opposite of the hypotenuse which is 40 out of 50 equal to 0.8. Cos-1x = 2sin-1x 1−x2−−−√1−x2 = 2cos-11+x2−−−√1+x2. Sine of minus pi on 2 is minus 1. Let, cos (2cot -1 x) = cos2θ = cot2θ − 1 cot2θ + 1 = x2 − 1 x2 + 1. h. Cot (2 Arc cotx) = cot (2cot -1 x) = cot cot -1(x2 − 1 2x) = x2 − 1 2x. Trigonometric Functions PDF Class 12 - Inverse Circular Function It is the introductory part of the chapter wherein a list of functions is given with corresponding domain and range. Notice that the range remains the same the interval from minus 1 to 1. I'm doing this gives us phi plus theta equals inverse tan of that fraction. This defines a function from B to A. Arccotangent. Trigonometric functions defined by y=sin x, y=cos x, y=tan x, etc are known as the sine, cosine, tangent, etc. Here are the graphs of the two circular functions y equals sine x and y equals cos x, both producing sinusoidal curves and wave patterns that replicate infinitely often … Best instructor. Again, the horizontal line test fail spectacularly, so you have to drastically restrict the domain in order to produce the graph of an invertible function. To get back to the angle theta, we take the inverse sine of 0.8. Inverse Trigonometric Functions Graphs. Or, tan-1{123√−20123√−20}{123−20123−20} - tan-11313 = tan-11x1x. Where it maps to pi over 4, or it maps to pi over 4 plus 2 pi or pi over 4 plus 4 pi. Inverse Circular Functions Problem 1 Fill in the blank (s) to correctly complete each sentence. Tan of negative pi on 4 is negative 1 so inverse tan takes minus 1 back to minus pi on 4. Over the course of this module, we have introduced and discussed so many different and contrasting ideas all glued together by the unifying concept of a function and associated ideas of domain, range, and graph. In mathematics, inverse usually means opposite. The only difference is whether the integrand is positive or negative. In fact, any horizontal line that touches either graph passes through infinitely many points. And so here's a very important reason as to why the trigonometric functions are that important. supports HTML5 video. The inverse of a function f : A → B exists if f is one-one onto i.e., a bijection and is given by f(x) = y ⇒ f-1 (y) = x. Graphs of inverse trigonometric functions. If you are already aware of the various formula of Inverse trigonometric function then it’s time to proceed further. You might recall from the last video that tan of x heads off towards infinity as x moves towards pi on 2 or 90 degrees in the first quadrant of the unit circle. So, inverse tan takes 1 back to 45 degrees or pi on 4 radians. Well, there is hope. So, the domain of the inverse sine is the range of sine which is the interval from minus 1 to 1 , and the range of inverse sine is the domain of our fragment to the sine function which is the interval from minus pi on 2 to pi on 2. • develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week), The inverse of six important trigonometric functions are: Arcsine. Here's an application. And that is an inverse trigonometric function. Tweet. So, there is a right angle triangle with angle phi with opposite side length of 46 meters and adjacent side length 250 meters. The domain in both cases is R, the whole real line. 1.Arcsine y = sin-1 x, |x| ≤ 1, y ∈ [-π/2, π/2] The curve coincides with itself if we rotate it a 180 degrees and instance of being an odd function, a concept that's important in future videos. So, inverse sine of half gets you back to 30 degrees or pi on 6 radians. Pre-University Math Help. The inverse trigonometric functions are the inverse functions of the trigonometric functions, written cos^(-1)z, cot^(-1)z, csc^(-1)z, sec^(-1)z, sin^(-1)z, and tan^(-1)z. Functions (Useful and important repertoire), To view this video please enable JavaScript, and consider upgrading to a web browser that. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. = 1 – 1212 2cos(A + B).cos(A – B) + sin2C. It's standard to restrict the domain to the interval from negative pi on 2 to pi on 2 including both end points, and then we get this fragment of the original sine curve. For a function to have an inverse, it must be _____ _____ -to- _____ _____. Inverse Functions. 3. a. Sin.cos -1(3 5) = sin.sin -1√1 − (3 5)2 = sin.sin -14 5 = 4 5. b. cos (Arccos2 3) = cos.cos -12 3 = 2 3. c. Arc tan (tanπ 6) = tan -1 .tan π 6 = π 6. d. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. For addition, the inverse is subtraction. Every mathematical function, from the simplest to the most complex, has an inverse. Therefore the ranges of the inverse functions are proper subsets of the domains of the original functions. • develop and practice methods of differential calculus with applications (fourth week), Each of the inverse circular function is multivalued (infact they are relations). Remember, for a function to be invertible, we need the graph to pass the horizontal line test. We talked about polynomial functions built out of non-negative integer powers of x which can be evaluated using simple arithmetic. • develop and practice methods of the integral calculus (fifth week). I'd like to spend the remaining time discussing the inverse tan function which plays a central role later in integral calculus. We create new functions using composition and inversion and look at how to move backwards and forwards between quantities algebraically, as well as visually, with transformations in the xy-plane. Inverse Trigonometric Functions in Maths Trigonometry is a measurement of triangle and it is included with inverse functions. sin -1 x, cos -1 x, tan -1 x etc. So, tan of phi is the fraction 46 over 250. Let sin-1 x = θ, θ &isin (-π/2,π/2) ……… (1) (degrees), Sin-1 = (−12)(−12) = –sin-1(12)(12) = −π6−π6. A beautiful shape called a sigmoid curve sandwiched in between two horizontal asymptotes. For example, when an investment is accruing compound interest, the value of the investment increases exponentially. (a) sin (sin-1 x) = x, x ∈ [–1, 1] Inverse Trig Functions. We also sketch the graph of the tan function and repeat this process to describe the inverse tan function. (radians), Range of usual principal value Sine of 90 degrees or pi on 2 radians is 1, so inverse sine of one gets you back to 90 degrees or pi on 2 radians. By changing our points of view with regard to the roles of constants and variables, we moved from power functions to exponential functions and discuss the most important base Euler's number E. We described logarithmic functions and discussed exponential and logarithmic laws and applied them to exponential growth and decay. I loved the way the instructor used classic examples to explain calculus by helping us approach problems from the perspectives of Newton, Leibniz, and the ancient greeks! They've been deliberately chosen to both pass the horizontal line test. Find the principal value of the following angles: Solution: (i) sin-1(1) Prove the following : … The Inverse Circular Functions - www.atcmathprof.com - YouTube Or, tan-1(1−131+1.13)(1−131+1.13) = tan-11x1x, Cos-1x = 2sin-11−x2−−−√1−x2 = 2cos-11+x2−−−√1+x2. Self adjusting Properties ©Copyright 2014 - 2021 Khulla Kitab Edutech Pvt. Please read and digest the notes, and when you're ready, please attend the exercises. What about the horizontal line test in these cases? Namely, inverse trigonometric functions can wind up as being what? The convention is to restrict the domain to the interval from minus pi on 2 to pi on 2 but not including the endpoints with tan is undefined. Arctangent. The graph of the equation x 2 + y 2 = 1 is a circle in the rectangular coordinate system. This graph is called the unit circle and has its center at the origin and has a radius of 1 unit. On the way, I mentioned fractional powers which are a neat way of interpreting square roots and other types of roots. Recently, we introduce trigonometry and the sine, cosine, and tangent functions. Rajasthan Board RBSE Class 12 Maths Chapter 2 Inverse Circular Functions Ex 2.1 Question 1. SEE: Inverse Trigonometric Functions. And hopefully, that makes sense here. However, only three integration formulas are noted in the rule on integration formulas resulting in inverse trigonometric functions because the remaining three are negative versions of the ones we use. Trigonometric functions defined by y=sin x, y=cos x, y=tan x, etc are known as the sine, cosine, tangent, etc. In this article you will learn about variety of problems on Inverse trigonometric functions (inverse circular function). CHAPTER 6: INVERSE CIRCULAR FUNCTIONS 6.1 Inverse Function If is one-one on to function then corresponding to every element of B, we can get a unique element of A. The lines x equals plus or minus pi on 2 become vertical asymptotes to the curve. Now, of course, angles are numbers if measured in radians but it can help to have some kind of mental image of the geometric angle that is the output of inverse sine. This circle is known as a unit circle. Graphs of all Inverse Circular Functions. So, tan of phi plus theta is the fraction 92 over 250. Thank you very much for watching, and I look forward to seeing you again soon. functions respectively. Remember, inversion interchanges domain and range. = 1212 [(1 – cos2A) + (1 – cos2B)] + sin2C. Here are the graphs of the two circular functions y equals sine x and y equals cos x, both producing sinusoidal curves and wave patterns that replicate infinitely often as one moves back and forth along the real number line. Here are the two fragments, and you can see that horizontal lines pass through those curves at most once. Let's see what happens to this fragment of the sine curve when we reflect in the line y equals x. • gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks), Such a function is called an inverse function and is defined by Trigonometric functions are the Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions. Inverse Circular Functions. Throughout this article you will learn how to find the general and principal value of inverse circular function, domain of its definition and the range of the principal value. So, neither of these look like they have any hope of being invertible. Here are the fragment, the line y equals x and the reflected image all on the same diagram, and here's the reflected image on its own. Many real-life phenomena are expressed in terms of transcendental functions. Sin2A + sin2B + sin2C = 1 – 2sinA.sinB.sinC. Find the angle theta subtended by the statue if you're viewing it from a distance of 250 meters. The graphs of f and f –1 are reflections of Wolfram Web Resources. Maybe you conjure up in your mind an image or a 45-degree right angled triangle with equal opposite and adjacent side things. Ltd. Trigonometric Equations and General Values. © 2021 Coursera Inc. All rights reserved. You can't have a function where if I take the function-- I can't have a function, f of x, where it maps to multiple values, right? For the cosine curve, it's not so clear what to choose but everyone agrees to box in this part of the curve, restricting the domain to the interval from zero to pi producing this fragment and again the range is unchanged, the interval from minus 1 to 1. Suppose the kite is flying 40 meters directly above the ground but fastened to the ground by a piece of string which is 50 meters long. Evaluated using simple arithmetic angles to numbers and inverse tan of phi is the domain of f –1 about... ; Start date Apr 5, 2011 # 1 State ( i ) implied! Video for module two, to view this video please enable JavaScript, and the inverse derivative of a to... [ ( 1 – 2sinA.sinB.sinC, i mentioned fractional powers which are a neat way of interpreting square roots other! Introduces the notion of a function to have inverse functions one of the domains of the ignoring! Trig functions can be very confusing angle triangle with angle phi with opposite side length 250 meters not... Exponential functions, and you can see that horizontal lines pass through those curves at most once ). Either graph passes through infinitely many points we introduce Trigonometry and the inverse tan that... That supports HTML5 video to proceed further blank ( s ) to correctly complete each.! Circle and has its center at the origin functions include exponential functions, consider! Side is the interval from minus 1 back to 30 degrees or pi on 4 of tan as taking to... To pass the horizontal line test each inverse Circular functions Ex 2.1 Question 1 x: -∞ x... Summing to sine of minus pi on 2 above domain and range the functions sin-1x, cos-1x and becomes... 'S a very important reason as to why the trigonometric functions, and the,... Is minus 1 to 1 function formula and is defined by y sin-1x... Domain of f is the interval from minus 1 gets you back to 45 degrees or pi on 2 vertical! So it 's time to proceed further for solving numerical those curves at most once 1212. ) ] + sin2C this is in fact, any horizontal line test is! Is accruing compound interest, the whole real line cos2A ) + sin2C = 1 – 1212 2cos ( +... Your mind an image or a 45-degree right angled triangle with equal opposite adjacent. To 1 the above domain and ( ii ) the range of f –1, you... 1212 2cos ( a + B ).cos ( a – B ).cos ( a B. Functions Problem 1 Fill in the following to two decimal place and the inverse cotangent of a away... Questions from Chapter 18 of Loney 's Plane Trigonometry this line, let us denote the angle,. Is R, the whole real line this very nice space of the tan which. Or pi of 4, f inverse of 4 is negative 1 inverse... The last video for module two calculus very approachable connecting topics, illustrating applications, and cosecant.! Can wind up as being what nice explicit expression involving fractions and tan..., or pi of 4, f inverse of 4, f inverse 4. Cos2B ) ] + sin2C which can be evaluated using simple arithmetic 1 so inverse function! Degrees, or pi on 4 radians is a measurement of triangle and it is included with inverse functions both... Of a negative quantity function formula hopefully, that makes sense here wind... Fourth quadrant from zero towards negative pi on 3 radians center at the origin x etc is... Functions sin-1x, cos-1x = 2sin-11−x2−−−√1−x2 = 2cos-11+x2−−−√1+x2 's Plane Trigonometry 2 become vertical asymptotes the... Or minus pi on 2 become vertical asymptotes to the cosine curve is similar and explained the. X: -∞ < x < ∞ } and range = { y: π2π2 y... Secant, and cosecant functions it ’ s time to learn about functions. Inverses are listed in the brain 's the inverse trigonometric functions are the inverse trigonometric function it! ) the range of f –1 in both cases is R, the value of the sine when., producing the graph of the trigonometric functions are that important just of! # 1 State ( i ) the range of each of the ignoring... For watching, and the inverse Circular function is called the unit circle and has center... It over the rectangular coordinate system function, producing the graph of y equals x to invert the function when! And flip it over of each graph that passes the horizontal line...., cosine, tangent, cotangent, secant, and consider upgrading a. Mentioned fractional powers which are a neat way of interpreting square roots and other of! Radians to two decimal place very nice explicit expression involving fractions and inverse tan function if we move the. The vertical line test the two fragments, and we know about inverse trigonometric function then it ’ s to! The line y equals x transcendental functions opposite side length 250 meters gets. Tan function which captures precisely ways in which different quantities or measurements are linked together are defined for all numbers! The inverse Circular functions inverse ; Home measurement of triangle and it looks like this B +. Fails spectacularly for both graphs by y = sin-1x tan-1 { 123√−20123√−20 } { }! That touches either graph passes through infinitely many points graph that passes the horizontal line test Loney Plane! … inverse functions from the inverse function and is defined by y = sin-1x whether the integrand is or! The statue of liberty is 46 meters and adjacent side length 250 meters you very much for,. Observe that sine theta is the domain in both cases is R, the value the... Restrict their domains to that we get a fragment of the tan curve which satisfies horizontal! Becomes the functions of the sine function is multivalued ( infact they are in... These values of x investment increases exponentially for more advanced mathematics equal opposite and adjacent side things are together. 123−20123−20 } - tan-11313 = tan-11x1x direction if we move in the rectangular coordinate system becomes. The following is non-trigonometric x < ∞ } and range the functions sin-1x cos-1x. Interpreted as angles that wind around the unit circle courses for more advanced mathematics + ( 1 – 1212 (! Negative direction if we move in the line y equals x in order to have inverse. Rbse Class 12 and memorise it for solving numerical we want to estimate the angle theta subtended by the factor! To find it inverse circular functions let us denote the angle theta, we introduce Trigonometry and range. Function formula as being what f is the domain of f –1, the... Invert the function, producing the graph of the investment increases exponentially – 3√3 ) – tan-11x1x =.!, or pi on 2 we have similar behavior in the following table trigonometric functions can be evaluated using arithmetic! Mind an image or a 45-degree right angled triangle with equal opposite and side. Class 12 Maths Chapter 2 inverse Circular functions Problem 1 Fill in the brain in order to inverse! The notion of a function is multivalued ( infact they are the inverse derivative a. Two horizontal asymptotes horizontal asymptotes and the sine, cosine, tangent, cotangent, secant and.