Solving Trig Equations Practice

 $Solve\ \ 3\sin x\ +\ 4\ =\ 6\ \ for\ \ 0\ \le\ x\ <\ 360\degree.$ Round to the nearest 10th of a degree.

•  $41.8\degree,\ 138.2\degree$  

•  $48.1\degree,\ 131.9\degree$  

•  $221.8\degree,\ 318.2\degree$  

•  $228.1\degree,\ 311.9\degree$  

 $Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360$  

•  $30\degree,\ 90\degree,\ 150\degree$  

•  $90\degree,\ 210\degree,\ 330\degree$  

•  $30\degree,\ 150\degree,\ 270\degree$  

•  $210\degree,\ 270\degree,\ 330\degree$  

   $Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree$  

•  $30\degree,\ 210\degree$  

•  $150\degree,\ 330\degree$  

•  $60\degree,\ 240\degree$  

•  $120\degree,\ 300\degree$  

• No solution
• π/3 +2πn, 5π/3 +2πn
• π/6 +2πn, 11π/6 +2πn
• 2π/3 +2πn, 4π/3 +2πn

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

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

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

•  $\theta=\frac{\pi}{6}$  

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

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

• π / 3
• 2π / 3
• 5π / 3
• 7π / 3

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

• TRUE
• FALSE

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔

Which is a correct way to solve the equation

cosx(2cosx − 3) = 0?

• divide cos x from both sides

• set each factor equal to 0 and solve

• distribute cosx into the parentheses

• guess and hope for the best

Solve equation for  $0\le\theta<2\pi$  .
 $2\sqrt{3}\sec\theta\cos\theta=-3\sec\theta$  

•  $\theta=\frac{5\pi}{6}$  

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

•  $\theta=\frac{7\pi}{6},\frac{4\pi}{3}$  

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