Trig Equations

TRUE or FALSE:
There is NO SOLUTION to sinθ = -1.

• TRUE
• FALSE

Tags

CCSS.HSF.TF.B.7

 $h\left(t\right)=10\ \cos\left(12\pi t\right)+25$  

A simple harmonic oscillator has displacement in cm, given by the equation above. What is the amplitude?

• 10 cm

• 15 cm

• 25 cm

• 35 cm

 $h\left(t\right)=10\ \cos\left(12\pi t\right)+25$  

A simple harmonic oscillator has displacement in cm, given by the equation above. What is the period?

• 0.1 s

• 0.167 s

• 0.333 s

• 0.5 s

 $h\left(t\right)=10\ \cos\left(12\pi t\right)+25$  

A simple harmonic oscillator has displacement in cm, given by the equation above. What is the frequency?

• 3 Hz

• 6 Hz

• 9 Hz

  
  
  

• 12 Hz

Solve  $\sin\theta=\frac{1}{2}$  on the interval,  $\left[0,\ 2\pi\right)$  

•  $\frac{\pi}{3},\frac{2\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $\frac{\pi}{6},\frac{7\pi}{6}$  

•  $\frac{4\pi}{3},\frac{5\pi}{3}$  

Solve equation for  $0\le\theta<2\pi$  .
 $1=5-8\cos\theta$  

•  $\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$  

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

•  $\theta=\frac{\pi}{6}$  

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

Tags

CCSS.HSF.TF.B.7

Solve  $\cos\theta=-\frac{2}{3}$  on the interval  $\left[0,2\pi\right)$  

• 2.3005, 3.9827

• 0.8401,  5.4421

• 3.2012, 3.3102

• 1.5707, 4.3421

Solve  $\sec^2\theta=4$  on the interval  $\left[0,2\pi\right)$  

•  $\frac{\pi}{3},\ \frac{2\pi}{3}$  

•  $\frac{2\pi}{3},\frac{4\pi}{3}$  

•  $\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$  

Solve  $2\sin\theta\cos\theta+\sin\theta=0$  on the interval  $\left[0,\ 2\pi\right)$  

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

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

•  $0,\frac{2\pi}{3},\pi\frac{4\pi}{3}$  

•  $\frac{\pi}{6},\frac{\pi}{2},\frac{5\pi}{6}$  

Solve  $2\sin^2\theta+\sin\theta-1=0$  on the interval  $\left[0,2\pi\right)$  

•  $\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}$  
  

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

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

•  $0,\ \frac{\pi}{6},\frac{7\pi}{6}$