inverse functions ### Understanding Inverse Trigonometric FunctionsWe have seen how the graph of the sine function is not one-to-one, and hence the inverse will not be a function.So, we limit the domain of the sine function on the interval \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\). Then it is one-to-one and still encompasses the entire range \(-1 \leq y \leq 1\). When we reflect across \(y = x\), we get the inverse sine function.#### Diagrams:1. **Reflection Visualization:** - A graph displays two functions. - The sine function is depicted in blue on the interval \([- \frac{\pi}{2}, \frac{\pi}{2}]\). - The red curve represents the inverse sine function, showing the reflection across \(y = x\). - Key points such as \((-\frac{\pi}{2}, -1)\) and \((\frac{\pi}{2}, 1)\) are highlighted.2. **Coordinate System for Tangent Function:** - Students are advised to draw a system similar to the provided example to explore the inverse tangent function. - This involves limiting the domain on the tangent function within the same interval and reflecting it over \(y = x\).#### Inverse Cosine Function:Unfortunately, the interval \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\) won’t work for the cosine function. We use the interval \(0 \leq x \leq \pi\).3. **Cosine Function Graph:** - Students are encouraged to use this interval to draw a graph of \(y = \cos x\). - Reflecting this over the line \(y = x\) will yield the graph of the inverse cosine function.Use these visual and conceptual guides to deepen your understanding of how inverse trigonometric functions are derived from their respective functions.

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We have seen how the graph of the sine function is not one to one, and hence the inverse will not be a function. So, we limit the domain of the sine function on the inverval < x<÷. Then it is one to one and still encompasses the entire range -1 < y< 1. When we reflect across y = x, we get the inverse sine function. -J On your own piece of paper, draw a coordinate system like the one below. Your task is to limit the domain on the tangent function on the same interval and then reflect it across the line y=x to obtain the inverse tangent function. Unfortunately, the interval –

We have seen how the graph of the sine function is not one to one, and hence the inverse will not be a function. So, we limit the domain of the sine function on the inverval < x<÷. Then it is one to one and still encompasses the entire range -1 < y< 1. When we reflect across y = x, we get the inverse sine function. -J On your own piece of paper, draw a coordinate system like the one below. Your task is to limit the domain on the tangent function on the same interval and then reflect it across the line y=x to obtain the inverse tangent function. Unfortunately, the interval –

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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