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Understanding Inverse Sine and Cosine Functions for Graphing

This resource provides a comprehensive guide on using your calculator to graph the inverse sine and cosine functions. Learn how to set your viewing window appropriately and use the 'DrawInv' command to visualize the inverse of the sine function. It covers important notations such as (y = sin^{-1}(x)) and (y = arcsin(x)), clarifying that both notations represent the same inverse function. Gain insights into the differences between inverse and reciprocal functions, ensuring a solid foundation in trigonometry.

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Understanding Inverse Sine and Cosine Functions for Graphing

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  1. 6.1.2 Inverse Sine and Cosine

  2. 6-21 • You can use your calculator to draw the full inverse of • sine by using the draw inverse command. Set your • window so that x goes from [−3, 3] and y goes from [−6, 6]. • Enter Y1 = sin−1(x) and graph the function. Now select • from the [DRAW] menu (2nd PRGM) and select 8: • DrawInv. On the main screen enter DrawInv sin(X). You • should see this graph cover up the function y = sin−1x.

  3. MATH NOTES - Notation for Inverse Trig Functions • There are two standard notations to represent the inverse for trig functions. • The first uses inverse notation. For example: y= sin−1x and y= cos−1x • You must be careful with this notation. The function y = sin−1x is not the • same function as y = . The function, y = is y= cscx, the reciprocal • function for sinx, while the function y = sin−1x is called the inverse function • for sin x. • Another form is using y = arcsinx for the inverse of sine and y = arccosxfor • the inverse of cosine. This notation, y = arcsinx can be thought of as “the • arc whose sine is …” This connects the inverse back to the unit circle. • Both y = sin−1x and y = arcsinx mean exactly the same thing.

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