Inverse Trigonometric Ratios &Sin & Cos of Complementary <s2

Inverse Trigonometric Ratios

You will learn how to use inverse trigonometric ratios to find a missing angle of a right triangle.

BUT FIRST...

Trigonometric Ratios Review

 $\sin\theta\ =\ \frac{opp}{hyp}$  

 $\cos\theta\ =\ \frac{adj}{hyp}$  

 $\tan\theta=\frac{opp}{adj}$  

Trigonometric Ratios help you find the measure of a missing side.

• First, identify the given angle.

• Second, identify each part of the triangle (opp, adj, and hyp) in reference to the given angle.

• Third, choose the appropriate trigonometric ratio based on the parts that are given.

• Fourth, plug in the numbers based on what is given.

• Finally, solve the ratio for the missing side.

Multiple Choice

Find the value of w. Round to the nearest tenth.

•  $9.2$ 

•  $19.0$ 

•  $11.7$ 

•  $24.4$ 

Multiple Choice

Find the value of h. Round to the nearest tenth.

•  $9.2$  

•  $24.4$  

•  $19.0$  

•  $11.7$  

Multiple Choice

Find the value of x. Round to the nearest tenth.

•  $44.1$  

•  $164.2$ 

•  $79.6$ 

•  $50.4$ 

Now let's look at Inverse Trigonometric Ratios - these are used to determine the measure of an angle in a right triangle

• sin^-1 (sometimes called arcsin)

• cos^-1 (sometimes called arccos)

• tan^-1 (sometimes called arctan)

• 
  

How do we use Inverse Trigonometric Ratios to find angles in a right triangle?

• Step 1: Identify the angle.

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

• Step 3: Identify the appropriate trigonometric ratio to solve for the missing angle.

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

Multiple Choice

Find the measure of angle A. Round to the nearest degree.

• 30°

• 60°

• 27°

• 63°

Multiple Choice

Find the measure of angle A. Round to the nearest degree.

• 22°

• 68°

• 27°

• 63°

Multiple Choice

What is the measure of the unknown angle? Round to the nearest angle.

• 53°

• 37°

• 51°

• 39°

Multiple Choice

What is the measure of the unknown angle? Round to the nearest degree.

• 74°

• 16°

• 78°

• 12°

Multiple Choice

What is the measure of the unknown angle? Round to the nearest degree.

• 31°

• 59°

• 37°

• 53°

Trigonometric Ratios of Complementary Angles

• When angles are complementary (add up 90°) their sine and cosine values are related.

• Let's look at an example.

• 
  

• 
  

So, in conclusion......

• sin and cos values of complementary angles are equal

• sin θ = cos (90 - θ)

Multiple Choice

• 76°

• 14°

• 104°

• 166°

Multiple Choice

• 52°, 0.788

• 38°, 0.788

• $52\degree,\ 0.616$

• $38\degree,\ 0.616$

Multiple Choice

• 26°, 0.899

• 64°, 0.899

• 26°, 0.438

• 64°, 0.438

Multiple Choice

Cos 30° = Sin ______

• 30°

• 60°

• 90°

• 45°