Applying and analysing trigonometric functions

Find the exact value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ . 

•  $\frac{\pi}{6}$  

•  $\frac{3\pi}{4}$  

•  $\frac{2\pi}{3}$  

•  $\frac{5\pi}{6}$  

Solve for x. cos(2x +9) = sin(x)

• x = 27

• x = -9

• x = 57

• x = 9

• DNE

• 0

•  1

• -1

Find x rounded to the nearest tenth.

• 46.1

• 4.9

• 16.4

• 26.9

 $Solve\sin x=\frac{\sqrt{3}}{2}\ ​for\ 0≤x≤360°$  

• 30, 150
  

• 60, 300
  

• 30, 330
  

• 60, 120
  

Solve  $\tan\theta=-\frac{\sqrt{3}}{3}$  for $0\le\theta<2\pi$  .

•  $\frac{2\pi}{3},\ \frac{5\pi}{3}$  

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

•  $\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\frac{5\pi}{6},\ \frac{11\pi}{6}$  

Solve the trigonometric equation in the interval  $\left(0,\ 2\pi\right]$ .

 $11\sin x+5=\sin x$  

•  $\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$  

Solve for x.

• 24.20
• 4.92
• 290.4
• 29.75

Which of the following are the correct solutions for the trigonometric equation in the interval  $\left(0,\ 2\pi\right]$ ? 

CHOOSE ALL THAT APPLY

 $14\sin^2x+21\sin x+7=0$  

•  $\frac{3\pi}{2}$  

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

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\frac{\pi}{2}$