solving trig equations

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

 $2\sin\theta\cos\theta-\sqrt{2}\cos\theta=0$  

•  $45\degree$  

•  $90\degree$  

•  $135\degree$  

•  $270\degree$  

•  $315\degree$  

Tags

CCSS.HSF.TF.B.7

 $Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree$  

•  $x\ =\ 60\degree,\ 120\degree$  

•  $x\ =\ 60\degree,\ 300\degree$  

•  $x\ =\ 30\degree,\ 150\degree$  

•  $x\ =\ 30\degree,\ 330\degree$  

Tags

CCSS.HSF.TF.B.7

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

•  $0,\ \pi$  

•  $\frac{\pi}{2},\ \frac{3\pi}{2}$  

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

• No solution

Tags

CCSS.HSF.TF.B.7

 $Solve\ \ \ 3\sec^2x\ =\ 4\ \ for\ \ 0\ \le\ x\ <\ 2\pi$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

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

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

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

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

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

Tags

CCSS.HSF.TF.B.7

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

•  $41.8\degree,\ 138.2\degree$  

•  $48.1\degree,\ 131.9\degree$  

•  $221.8\degree,\ 318.2\degree$  

•  $228.1\degree,\ 311.9\degree$  

Tags

CCSS.HSF.TF.B.7

 $Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$  

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

•  $0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$  

•  $\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$  

•  $0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

Solve
cos²θ = ½ 
on θ∈[0, 2π)

• θ = π /4, 7π /4
• θ = π /4, 3π /4
• θ = 3π /4, 5π /4
• θ = π /4, 3π /4, 5π /4, 7π /4

Tags

CCSS.HSF.TF.B.7

 $3\sin\ x\ +\ 1\ =\ \sin\ x$  

•  $x=\frac{7\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{11\pi}{6}+2\pi n$  

•  $x=\frac{\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{5\pi}{6}+2\pi n$  

•  $x=\frac{4\pi}{3}+2\pi n,\ \ \ \ x=\frac{5\pi}{3}+2\pi n$  

•  $x=\frac{\pi}{4}+\pi n$  

Tags

CCSS.HSF.TF.B.7

 $\tan^2\ x=3$  

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

•  $x=\frac{\pi}{6}+\pi n,\ \ \ \ x=\frac{5\pi}{6}+\pi n$  

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

• No solution

Tags

CCSS.HSF.TF.B.7