Trig 3-3

Trig 3-3

Trigonometric Equations

Multiple Choice

Quick Check 1
Is  $\theta=\frac{\pi}{6}$   a solution of the equation  $2\sin⁡θ-1=0$  ? If so, is it the only solution?

• No. It is not a solution

• Yes, and it is the only solution.

• Yes. And there are infinitely many solutions! 

• Yes. And there are exactly 4 solutions. 

Multiple Choice

Quick Check 2

Use a calculator to solve the equation  $\sin⁡θ=-0.98$  on the interval  $0\le\theta<2\pi$ . 

Hint:  $\pi-\theta$  and  $2\pi+\theta$  might be helpful! 

•  $4.512$  and  $4.913$  

•  $1.77$  and  $1.37$  

•  $-1.37$  and  $8.054$  

•  $-4.913$  and  $4.913$  

Multiple Choice

Quick Check 3

Rewrite the following equation using identities so that the quadratic method can be used to solve:  $\sec^2\theta+\tan\theta=0$ . 

•  $\tan^2-\tan\theta-1=0$  

•  $\sec^2\theta-\sec\theta-1=0$  

•  $\tan^2\theta+\tan\theta-1=0$  

•  $\tan^2\theta+\tan\theta+1=0$