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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.

Feb 23, 2012

Nov 04, 2014