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5.1: What’s your Inverse?

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Trigonometry, Chapter 4, Lesson 3.

Problem 1

Press Y= and graph Y1 = \sin^{-1} x. Press MODE and make sure Radian is highlighted. Press GRAPH.

  • Press ZOOM, 7:ZTrig. Graph and determine the domain and range of the function.
  • Why is there a restricted domain on this function?

Problem 2

Press Y= and graph Y1 = \cos^{-1}x. Press GRAPH.

  • Graph and determine the domain and range of the function.

Problem 3

Press Y= and graph Y1 = \tan^{-1}x. Press 'GRAPH.

  • Graph and determine the domain and range of the function.

For secant, cosecant and cotangent, it is a little more difficult to plug into Y=.

Problem 4

Prove \cos^{-1}x=\sec^{-1}\left(\frac{1}{x}\right). This will be how you graph y=\sec^{-1}x in the graphing calculator.

  • Graph your results from above in Y=. Find the domain and range of the function.

Problem 5

Prove \sin^{-1}x=\csc^{-1}\left(\frac{1}{x}\right). This will be how you graph y=\csc^{-1}x in the graphing calculator.

  • Graph your results from above in Y=. Find the domain and range of the function.

Problem 6

Tangent and cotangent have a slightly different relationship. Recall that the graph of cotangent differs from tangent by a reflection over the y-axis and a shift of \frac{\pi}{2}. As an equation, it would be \cot \ x=-\tan \left(x-\frac{\pi}{2}\right). Take the inverse of y=-\tan \left(x-\frac{\pi}{2}\right).

  • Graph your results from above in Y=. Find the domain and range of the function.

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Date Created:

Feb 23, 2012

Last Modified:

Nov 04, 2014
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TI.MAT.ENG.SE.1.Trigonometry.5.1

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