Week 2 Quiz: Solving Sine and Cosine Equations

Which of the following would have a domain error?

• $\sin^{-1}\left(-0.6\right)$

• $\cos\left(\frac{8}{9}\right)\$

• $\cos^{-1}\left(2\right)$

• $\tan2$

What angle (between $0^o$ and  $180^o$ ) has a sine value of  $0.4$  ? Round your answer to the nearest degree.

What angle (between $0^o$ and  $180^o$ ) has a cosine value of  $-0.11$  ? Round your answer to the nearest degree.

Solve for $\theta$  using a calculator. 
 $2\sin\theta=1.7$  

•  $58^o$  

• Domain Error

•  $32^o$  

•  $-17^{o\ }$  

Solve for $\theta$  using a calculator. 
 $4\cos\theta+4=1$  

•  $-139^o$  

•  $-76^{o\ }$  

•  $139^o$  

•  $76^{o\ }$  

Select 2 possible values for $\theta$  given  $8\sin\theta=-4.$  

•  $\frac{\pi}{6}$  

•  $\frac{5\pi}{6}$  

•  $\frac{7\pi}{6}$  

•  $\frac{11\pi}{6}$  

Select 2 possible values for $\theta$  given  $\cos\theta=\frac{\sqrt{3}}{2}.$  

•  $\frac{\pi}{6}$  

•  $\frac{5\pi}{6}$  

•  $\frac{7\pi}{6}$  

•  $\frac{11\pi}{6}$  

Select all possible values for $\theta$  if  $7\sin^2\theta-3=4.$  

•  $0$  

•  $\frac{\pi}{2}$  

•  $\frac{3\pi}{2}$  

•  $2\pi$  

Which of the following is NOT a possible value of $\theta$  if  $\cos^2\theta=\frac{1}{4}.$  

•  $\frac{\pi}{3}$  

•  $\frac{3\pi}{2}$  

•  $\frac{4\pi}{3}$  

•  $\frac{5\pi}{3}$  

If  $\sin^2\theta=\frac{1}{2}$  , how many possible values of  $\theta$  are there between  $0$  and  $2\pi$  ?

• 0

• 1

• 2

• 4