Unit 7 Lesson 1

Trigonometric Functions and Acute Angles

Unit 7 Lesson 1

Open Ended

Bellwork

Research: How are Trig Functions used in real life?

Just Remember

 $\sin\theta=\frac{opposite}{hypotenuse}$  

 $\cos\theta=\frac{adjacent}{hypotenuse}$  

 $\tan\theta=\frac{opposite}{adjacent}$  

Multiple Choice

What are the trigonometric ratios of an angle with measure θ

theta in a right triangle given the following?

Step 1: Which triangle is labeled correctly?

Multiple Choice

What are the trigonometric ratios of an angle with measure θ

theta in a right triangle given the following?

Step 2: Find the missing side using the Pythagorean Theorem. Which triangle gives the correct side length?

Multiple Choice

What are the trigonometric ratios of an angle with measure θ

theta in a right triangle given the following?

Step 3: Use the right triangle to find other trig ratios. What is the cosθ?

• $\frac{25}{7}$

• $\frac{24}{7}$

• $\frac{7}{24}$

• $\frac{7}{25}$

Multiple Choice

The sun shines at a 60 degrees angle to the ground. How long is the shadow cast by a 20 ft tall flagpole?

Step 1: Which image correctly illustrates this scenario?

Multiple Choice

The sun shines at a 60 degrees angle to the ground. How long is the shadow cast by a 20 ft tall flagpole?

Step 2: Which trig function should you use to build your equation?

• Sine

• Cose

• Tangent

Multiple Choice

The sun shines at a 𝟨𝟢° angle to the ground. How long is the shadow cast by a 20 ft tall flagpole?

Step 3: Write an equation to represent the scenario.

• $\tan60\degree=\frac{20}{x}$

• $\tan60\degree=\frac{x}{20}$

Lesson Review

Multiple Select

Knowing that $\cos\theta=\frac{5}{13}$   , which of the following are other trigonometric ratios for θ? Select all that apply.

•  $\sin\theta=\frac{13}{5}$  

•  $\tan\theta=\frac{12}{5}$  
  

•  $\sec\theta=\frac{13}{5}$  
  

•  $\csc\theta=\frac{13}{12}$  

•  $\tan\theta=\frac{5}{12}$