Trig Equations with Pythagorean Identities

1/24 Solving Trig Equations and Review

By Nichole Nuckols

Objective​

In this lesson, we will:

1. Solve a Trig equation using squaring the Pythagorean Identities

2. Review 6.1 and 6.2​

​Opening Activity

Complete the assigned 1/24 Warm-UP on Google Classroom.​

Example 1: Solving Trig Equation (Squaring)

​You can't combine like terms and converting to sine and cosine doesn't lead to any useful mathematics. So, we will square both sides and reduce to one trig function using a Pythagorean Identity. There will be extraneous solutions.

Check: Plug the solutions back into the original equation.

Example 2: Solving Trig Equation (Squaring)

Multiple Choice

Solve the equation for $$0\le\theta<360$$  .

$$-3\cos\theta=-\sqrt{3}\sin\theta-2\cos\theta$$  

• {30, 150, 210, 330}

• {30, 210}

• {30}

• {120}

Multiple Choice

Solve the equation for $$0\le\theta<360$$  .

$$-\tan\theta=\sqrt{2}\tan\theta+\sec\theta-\tan\theta$$   

• {45, 135, 225, 315}

• {225}

• {225, 240}

• {225, 315}

​Recall: Only One-to-One functions are inversible.

Multiple Choice

Find the exact value of the expression. $$\cot^{-1}\left(\cos\pi\right)$$  

• $$\frac{\pi}{6}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{3\sqrt{55}}{55}$$  

• $$\pi$$  

Multiple Choice

Find the exact value of the expression. $$\csc\cos^{-1}\ \frac{7}{12}$$   

• $$-\frac{\pi}{2}$$   

• $$\frac{\pi}{6}$$   

• $$\frac{12\sqrt{95}}{95}$$   

• $$\frac{7\sqrt{95}}{95}$$   

Thank you for your time and participation

No new assignments.

There will be a quiz on 1/26.​