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5.1: What’s your Inverse?

Difficulty Level: At Grade Created by: CK-12
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This activity is intended to supplement Trigonometry, Chapter 4, Lesson 3.

Problem 1

Press Y= and graph Y1=sin1x. 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=cos1x. Press GRAPH.

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

Problem 3

Press Y= and graph Y1=tan1x. 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 cos1x=sec1(1x). This will be how you graph y=sec1x in the graphing calculator.

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

Problem 5

Prove sin1x=csc1(1x). This will be how you graph y=csc1x 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 yaxis and a shift of π2. As an equation, it would be cot x=tan(xπ2). Take the inverse of y=tan(xπ2).

  • 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