Inverse Trig Functions

Inverse Trigonometric Ratios

​Dr. Tom Giles

Using Inverse Trigonometric Ratios to find missing angles of right triangles.

The trig ratios sin 𝜃 , cos 𝜃 , tan 𝜃 tell you the ratio between the matchings sides, which in turn can be used to find sides.

 Inverse trig is used to find missing angles. 

• sin^-1 (sometimes called arcsin or sinh on your phone calculators)

•  cos^-1 (sometimes called arccos or cosh)

•  tan^-1 (sometimes called…you guessed it…arctan or tanh)

How do we use Trig Functions to find missing angles?

• Step 1: Identify the angle

• Step 2: Label opp, adj, and hyp based on given angle

• Step 3: Identify the appropriate trig function to solve for the missing angle

• Step 4: Use sin^-1 , cos^-1 , tan^-1 to solve the equation for the angle 

Multiple Choice

To find a missing angle when given two sides, you must use ______

• Trigonometric Functions

• Trigonometric Rations

• Inverse Trigonometric Functions

• Pythagorean Theorem

Multiple Choice

Set up an equation that could be used to solve for the variable.

Multiple Choice

Set up an equation that could be used to solve for the variable.

Multiple Choice

What is the ratio for Cosine?

• Opp/Hyp

• Opp/Adj

• Adj/Opp

• Adj/Hyp

Multiple Choice

What is the ratio for Tangent

• Opp/Adj

• Adj/Opp

• Opp/Hyp

• Hyp/Opp

Multiple Choice

What is the ratio for Sine?

• Hyp/Opp

• Opp/Hyp

• Opp/Adj

• Adj/Opp

Multiple Choice

Find the measure of the angle. Round to the nearest tenth.

• 30.8

• 32.1

• 34.3

• 36.9

Multiple Choice

Choose the correct ratio.

• sin^-1(9/20)

• cos^-1(9/20)

• tan^-1(9/20)

• cos^-1(20/9)

Multiple Choice

Find the measure of angle A.

• 24

• 90

• 66

• 42

Multiple Choice

Find the measure of angle A.

• 24

• 90

• 66

• 42

Multiple Choice

Solve for the missing angle

• 50.5 degrees

• 12.7 degrees

• 36.9 degrees

• 72.2 degrees

Multiple Choice

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

• 49°

• 57°

• 45°

• 54°

Multiple Choice

Find the measure of the missing angle.

• 64^o

• 26^o

• 61^o

• 8^o