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Exploring Inverse Trigonometric Functions and Right Triangle Applications

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This document delves into inverse trigonometric functions with a focus on right triangle applications. It examines a scenario with a right triangle where one side measures 4 meters and the hypotenuse is 13 meters, determining the length of the other side and the measures of the two non-right angles. It also addresses practical applications, such as designing a wheelchair ramp with a target grade and height difference, and calculating the necessary angle and ramp length. Further exploration includes computing trigonometric values and simplifying expressions involving inverse functions.

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Exploring Inverse Trigonometric Functions and Right Triangle Applications

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  1. Math 170 Functions, Data, and Models 32 Inverse Trigonometric Functions Sections 7.5

  2. Inverse Trigonometric Functions • Consider a right triangle with one side 4 meters and hypotenuse 13 meters. What is the length of the other side and the values of the two non-right angles? • Do the trigonometric functions have inverses?

  3. Right Triangle Trigonometry • Find the side and angle measurements for the given triangles.

  4. Applications • 7.5 #38. You want to build a wheelchair ramp leading up to your house. Your front door is 2 feet higher than the driveway and you would like the grade of the ramp to be 7%. • What is the angle that the ramp forms with the driveway? • How long does the driveway have to be to build this ramp? • How long will the ramp be? • 7.5 #42. A staircase is to rise 17.3 feet over a horizontal distance of 10 feet. At approximately what angle with respect to the floor should it be built?

  5. 2. Let arcsin4/5 = x. Compute the following without using a calculator. (a) cos x (b) tan x ConcepTest• Section 7.5•Question 2

  6. 3. Simplify sin(arctan x) as an expression that involves only the term x. ConcepTest• Section 7.5•Question 3

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