Mathwarehouse Logo

Inverse Sine, Cosine and Tangent

The inverse of SOHCAHTOA

Inverse Trig Functions Worksheet
Inverse Cosine Calculator
Inverse Sine Calculator

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

Inverse Trigonometry

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 angle symbol LNM?

Since the total measure of the interior angles of a triangle is 180 degrees we can verify the measure of angle symbol LNM:
direction arrow 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.

sin-1(73.24/76.19) = 74°

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.

Example Problem

To find the measure of $ \angle CAB$, the shaded angle, consider the sides that we know.

Compare sine with inverse sine.

inverse sine, SOHCAHTOA
$ sin(b)$
$$ sin (b) = \frac{ac}{ab} $$ Sine of angle outputs the ratio of 2 sides of a triangle
$ sin^{-1}(b)$
$$ sin^{-1} \left( \frac{ac}{ ab} \right) = m\angle ABC $$ Inverse sine of 2 sides outputs an angle measurement

Practice Problems

Problem 1
Inverse Sine Problem

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

tan-1(24/18) = 53°
Problem 2
Inverse Sine Picture

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

tan-1(5/12) =23°
Problem 3
Inverse sine diagram

What is the measure of the shaded angle on the left?

sin-1(36/39) = 67°
Problem 4
inverse cohcahtoa

What is the measure of angle c in the triangle below? Round your answer to the nearest tenth of a degree.

Since you know all 3 sides, you could use any of the following:

angle c = sin-1(7/25) = 16.3°
angle c = cos-1(6/15) = 16.3°
angle c = tan-1(7/24) = 16.3°
Problem 5
inverse sohcahtoa

Use inverse sohcahtoa to calculate the measure of angle a in the triangle below. Round your answer to the nearest hundredth of a degree.

Since you know all 3 sides, you could use any of the following:

angle a = sin-1(8/10) = 53.13°
angle a = cos-1(6/10) = 53.13°
angle a = tan-1(8/6) = 53.13°
Related:
Back to SOHCAHTOA Side lengths Next to SOHCAHTOA to find side lengths

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!