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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 –

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Trigonometric Functions: Right Triangle Approach
Section5.4: Inverse Trigonometric Functions And Right Triangles
Problem 1E: For a function to have an inverse, it must be ___________. To define the inverse sine function, we...
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inverse functions

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 s y< 1. When we reflect across y = x, we get the inverse sine function. 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 –<x< won't work for the cosine function. We use the interval 0 < x < n. On your own piece of paper, draw a coordinate system like the one below. Then draw a graph of y = cos x on this interval and then reflect over the line y =x to obtain the graph of the inverse cosine function.
Transcribed Image Text: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 s y< 1. When we reflect across y = x, we get the inverse sine function. 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 –<x< won't work for the cosine function. We use the interval 0 < x < n. On your own piece of paper, draw a coordinate system like the one below. Then draw a graph of y = cos x on this interval and then reflect over the line y =x to obtain the graph of the inverse cosine function.
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