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Inverse Sine, Cosine and Tangent
The inverse of SOHCAHTOA
Compare sine with inverse sine.
Inverse or sin-1 is an operation that uses the same two sides of a right triangle as sine does (opposite over hypotenuse) in order to find the measure of the angle (in this case b)
- sin-1(AC/AB) = measure of angle B
Key difference: Although both sine and inverse sine involve the opposite side and hypotenuse of a right triangle, the result of these two operations are very, very different. One operation (sine) finds the ratio of these two sides; the other operation, sine inverse, actually calculates the measure of the angle (B in the example above) using the opposite side and the hypotenuse.
Practice Problems
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Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
tan-1(24/18) = 53°
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Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
tan-1(5/12) =23°
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What is the measure of the shaded angle on the left?
sin-1(36/39) = 67°
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LNM?
180° -16° - 90° =74 °