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RedAssign2[1].5

# RedAssign2[1].5 - increasing and therefore one-to-one You...

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Unit: Elementary Functions and Their Inverses Module: Inverse Trigonometric Functions The Inverse Sine, Cosine, and Tangent Functions www.thinkwell.com Copyright 2001, Thinkwell Corp. All Rights Reserved. 1562 –rev 06/13/2001 The standard trigonometric functions do not have inverses . Only by restricting the domain can you make them one-to-one functions. The inverse trig functions can be indicated by a raised –1 or by the prefix ”arc”. The sine, cosine and tangent functions do not pass the horizontal line test . Therefore they do not have inverses . Despite that fact, it would be useful to find a way to define inverse trigonometric functions. Notice that from – π /2 to π /2 the sine function is increasing. On this restricted domain sine is one- to-one . You can find other domains where sine is also
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Unformatted text preview: increasing and therefore one-to-one. You can even find domains where it is decreasing. The sine function will be one-to-one there, too. You can define lots of inverses for the sine function. However, mathematicians established a convention to use [– π /2, π /2] for the standard inverse sine function. Here are the graphs of the inverses of sine, cosine, and tangent. They are labeled arcsine , arccosine , and arctangent , respectively, instead of using the –1 notation. Notice that arccosine is defined by a different interval than the others. The cosine function is restricted to the interval [0, π ] in order to define its inverse. Tangent is restricted to [– π /2, π /2], just like sine. The vertical asymptotes for tangent are translated into horizontal asymptotes for arctangent....
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