Introduction to Trigonometry

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:  $$\sec^2\theta+\tan\theta=0$$ . 

• $$\tan^2-\tan\theta-1=0$$  

• $$\sec^2\theta-\sec\theta-1=0$$  

• $$\tan^2\theta+\tan\theta-1=0$$  

• $$\tan^2\theta+\tan\theta+1=0$$