5.8. Graphs of Inverse Trigonometric Functions http://www.ck12.org
5.8 Graphs of Inverse Trigonometric Functions
Here you will graph the final form of trigonometric functions, the inverse trigonometric functions. You will learn
why the entire inverses are not always included and you will apply basic transformation techniques.
In order for inverses of functions to be functions, the original function must pass the horizontal line test. Though
none of the trigonometric functions pass the horizontal line test, you can restrict their domains so that they can
pass. Then the inverses are produced just like with normal functions. Once you have the basic inverse functions,
the normal transformation rules apply.
Why is sin−^1 (sin 370◦) 6 = 370 ◦? Don’t the arcsin and sin just cancel out?
Watch This
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/61270http://www.youtube.com/watch?v=bBBUMHe900U Inverse Trigonometric Functions
Guidance
Since none of the six trigonometric functions pass the horizontal line test, you must restrict their domains before
finding inverses of these functions. This is just like the wayy=√xis the inverse ofy=x^2 when you restrict the
domain tox≥0.
Consider the sine graph: