# Inverse Functions Worksheets

What Are Inverse Functions? The word trigonometry is derived from the Greek words trigonon, meaning triangle, and metron meaning measure. It is defined as the branch of mathematics that establishes the relationship between the angles and sides. Trigonometry is not only used for solving triangles, but many other straight-sided shapes are simplified into a collection of triangles. Moreover, strangles is also related to other branches of mathematics like infinite series, calculus, and complex numbers. Trigonometry helps us in finding the missing sides and angles by using the trigonometric ratios. These ratios are mainly measured in degrees and radians. The three known and commonly used Inverse Functions are sine cosine and tangent, which are abbreviated as sin, cos, and tan, respectively. Apart from these three functions, trigonometry also uses three other functions, namely cosec, sec, and cot. These three other functions are the inverse functions of sine, cosine, and tangent functions. The six Inverse Functions are defined below: Sine: It is defined as the ratio of the opposite side to the hypotenuse of the right-angled triangle. Cosine: It is defined as the ratio of the adjacent side to the hypotenuse of the right-angled triangle. Tangent: It is defined as the ratio of the opposite side to the adjacent of the right-angled triangle. Cosec: It is defined as the ratio of the hypotenuse to the opposite side of the right-angled triangle. Sec: It is defined as the ratio of the hypotenuse to the adjacent side of the right-angled triangle. Cot: It is defined as the ratio of the adjacent side to the opposite side of the right-angled triangle. Trigonometry is one of the most important areas in the mathematical branch of geometry. These functions are used to describe the function between sides and angles of a right triangle. There are six basic trigonometric functions, and these include Sine, Cosine, Tangent, Cosecant, secant, and cotangent. To define these functions, we can use a unit circle. We know that; The sine of an angle is the ratio of the opposite to the hypotenuse. The cosine of an angle is the ratio of the adjacent to the hypotenuse. The tangent of an angle is the ratio of the opposite to the adjacent. The cotangent of an angle is the ratio of the adjacent to the opposite The secant of an angle is the ratio of the hypotenuse to the adjacent leg. The cosecant of an angle α is the ratio of the hypotenuse to the opposite. Then there are the inverse trigonometric functions; these functions are opposite of regular trigonometric functions such as; Inverse sine, represented by sin(-1)⁡x, does the opposite of the sine. Inverse cosine, represented by cos(-1)⁡x does the opposite of the cosine. Inverse tangent, represented by tan(-1)⁡x, does the opposite of the tangent.

• ### Basic Lesson

Guides students solving equations that involve an Inverse Functions. Is {(4,8),(5,6)} the inverse of the function {(8,4),(6,5)}? The inverse of a function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. In the above question the pair is interchanged hence it is the inverse of the function.

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems. Using composition of functions, show that f(x) = 2x-1 and g(x)= 5x+1 are inverse functions.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of the solving Inverse Functions.

• ### Independent Practice 2

Students find the value of Inverse Functions in assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of the Inverse Functions.

• ### Skill Quiz

This tests the students ability to evaluate math statements with the Inverse Functions.

• ### Answer Key

Answers for math worksheets, quiz, homework, and lessons.

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