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When working with trigonometric inverse problems, keep the following information in mind:
Inverse Notation: |
arcsin(x) = sin-1(x)
arccos(x) = cos-1(x)
arctan(x) = tan-1(x)
arcsin(x)is read "the angle
whose sine is x".
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Tangent is positive in Quadrant I. |
Solution:
You are looking for "the angle whose tangent is" and the angle is in the interval .
creates the triangle shown at the right. The Pythagorean Theorem was used to find the length of the hypotenuse.
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Sine is positive in Quadrant I.
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Solution:
You are looking for "the angle whose sine is" the same as the in the interval .
You need to find an angle whose
in .
Remember when f (f-1(x)) = x? This concept does not apply in this situation because of the restrictions on the domain of sine inverse. |
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For help with trigonometric inverses on
your calculator,
click here. |
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