Trig solving Review

Which of the following is NOT a solution to
 $\csc\ \theta=\frac{2}{\sqrt{3}}$ on  $\left[0,4\pi\right)$   ?

•  $\frac{\pi}{3}$  

•  $\frac{2\pi}{3}$  

•  $\frac{5\pi}{3}$  

•  $\frac{7\pi}{3}$  

Solve $\sin\theta=\frac{1}{2}$   over the interval [0, 2π)

•  $\theta=\frac{\pi}{6},\frac{7\pi}{6}$  

•  $\theta=\frac{\pi}{6},\frac{5\pi}{6}$  

•  $\theta=\frac{5\pi}{6},\frac{7\pi}{6}$  

•  $\theta=\frac{7\pi}{6},\frac{11\pi}{6}$  

 Solve $3\sec\left(\theta\right)\ =\ -6$ over the interval $\left[0,\ 2\pi\right)$  

•  $\theta\ =\frac{\pi}{3},\ \frac{2\pi}{3}$  

•  $\theta=\frac{\pi}{3},\frac{5\pi}{3}$  

•  $\theta=\frac{2\pi}{3},\frac{4\pi}{3}$  

•  $\theta=\frac{4\pi}{3},\frac{5\pi}{3}$  

Solve  $4\sin\left(x\right)+2\ =\ 2\sin\left(x\right)$  over  $\left[0,\ 2\pi\right)$  

•  $x=\frac{\pi}{2},\ \frac{3\pi}{2}$  

•  $x=\frac{\pi}{2}$  

•  $x=\frac{3\pi}{2}$  

•  $x=\pi$  

Which of these is NOT a solution to tan θ = 0 ?

• $\theta=0$

• $\theta=\frac{\pi}{2}$

• $\theta=\pi$

• $\theta=2\pi$

Find the complete solution for  $\sec^2\theta=2$  over [0, 2π)

•  $\theta=\frac{\pi}{4},\ \frac{7\pi}{4}$  

•  $\theta=\frac{\pi}{4},\ \frac{3\pi}{4}$  

•  $\theta=\frac{3\pi}{4},\frac{5\pi}{4}$  

•  $\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$  

Solve  $\sqrt{3}\cot\theta+3\ =0$ over $\left(-\infty,\ \infty\right)$   

•  $\theta=\frac{\pi}{3}+\pi k$ 

•  $\theta=\frac{2\pi}{3}+\pi k$  

•  $\theta=\frac{\pi}{6}+\pi k$  

•  $\theta=\frac{5\pi}{6}+\pi k$  

 Solve $2\sin x=\sin x$  on the Interval  $\left(-\infty,\ \infty\right)$  

• No Solution

•  $x=\frac{\pi}{2}+\pi k$  

•  $x=\pi k$  

•  $x=\frac{\pi}{6}+2\pi k;\ \frac{5\pi}{6}+2\pi k$  

Solve $2\csc\ \theta+4=0$  over the interval  $\left[0,\ 4\pi\right)$  

•  $\frac{7\pi}{6},\frac{11\pi}{6},\frac{19\pi}{6},\frac{23\pi}{6}$  

•  $\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6}$  

•  $\frac{\pi}{6},\frac{11\pi}{6},\frac{13\pi}{6},\frac{23\pi}{6}$  

•  $\frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6}$  

Solve $2\cos\theta+7=3$  over all reals.

•  $\theta=\frac{\pi}{3}+2\pi k,\frac{5\pi}{3}+2\pi k$  

•  $\theta=\frac{2\pi}{3}+2\pi k,\ \frac{4\pi}{3}+2\pi k$  

•  $\theta=\frac{5\pi}{6}+2\pi k,\ \frac{7\pi}{6}+2\pi k$  

• No Solution