﻿ Inverse Sine, Cosine & Tangent. How SOHCAHTOA can Calculate Angles. How to use these functions...

# 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.

### Inverse SOHCAHTOA Way 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?

Since the total measure of the interior angles of a triangle is 180 degrees we can verify the measure of LNM 180° -16° - 90° =74 °

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.

### YouTube Vid: How to Calculate Inverse SOHCAHTOA

A good video on how to use your a TI-Graphing Calculator to calculate the inverse sine,cosine or tangent.

#### Compare sine  with inverse sine. General Difference: sine is the ratio of two actual sides of a right triangle (the opposite & hypotenuse) sin(B) = AC/AB

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.

### PracticeProblems

##### Problem 1 Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.

tan-1(24/18) = 53°
##### Problem 2 tan-1(5/12) =23°
##### Problem 3 sin-1(36/39) = 67°
##### Problem 4 Since you know all 3 sides, you could use any of the following: = sin-1(7/25) = 16.3° = cos-1(6/15) = 16.3° = tan-1(7/24) = 16.3°
##### Problem 5 Since you know all 3 sides, you could use any of the following: = sin-1(8/10) = 53.13° = cos-1(6/10) = 53.13° = tan-1(8/6) = 53.13°

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