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Inverse Sine, Cosine and Tangent

The inverse of SOHCAHTOA

The inverse trigonometric functions (sin-1, cos-1, and tan-1) allow you to find the measure of an angle in a right triangle. All that you need to know are any two sides as well as how to use SOHCAHTOA.

Vs. Interior Angle Sum

Compare This Method To the tried and true theorem that the sum of the interior angles of a triangle is 180°.

What is the degree measure of LNM?
Interior Angle Sum Way


Alternately, you could use the inverse of one of the SOHCAHTOA functions, in this case the inverse of sine (sin-1)! To find, an angle of a right triangle all that we need to know is the length of two sides! Then use the same SOHCAHTOA ratios --just in a different fashion See the example below.
Inverse SOHCAHTOA Way


YouTube Vid: How to Calculate Inverse SOHCAHTOA

A good video on how to use your TI-Graphing Calculator to calculate the inverse sine,cosine or tangent.
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inverse sine, 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
Inverse Sine Problem Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
Angle's Measurement
Inverse Sine Picture Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
Angle's Measurement
Inverse sine diagram What is the measure of the shaded angle on the left?
Angle's Measurement
What is the measure of in the triangle below? Round your answer to the nearest tenth of a degree.
Angle's Measurement
Use inverse sohcahtoa to calculate the measure of in the triangle below. Round your answer to the nearest hundredth of a degree.
Angle's Measurement