Pre-Calculus: Solving Trigonometric Equations

 $\frac{\pi}{6}$  is a possible solution to the equation  $2\sin^2\alpha+3\sin\alpha-2=0$  

• True

• False

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

Solve the trigonometric equation:

 $4\sin^2\left(x\right)-3=0$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

Solve the trigonometric equation:

 $2\cos\left(x\right)+\sqrt{2}=0$  

•  $\frac{3\pi}{4},\frac{5\pi}{4}$  

•  $\frac{\pi}{4},\frac{3\pi}{4}$  

•  $\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\frac{\pi}{2},\ \frac{3\pi}{2}$  

Tags

CCSS.HSF.TF.B.7

Solve the following trigonometric equation:

 $\sec\left(x\right)+2=0$  

•  $\frac{\pi}{3},\frac{5\pi}{3}$  

•  $\frac{2\pi}{3},\frac{4\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $0,\pi$  

Tags

CCSS.HSF.TF.B.7

Solve the trigonometric function:

 $-2-3\sin\left(x\right)=1-6\sin\left(x\right)$  

•  $0$  

•  $\frac{3\pi}{2}$  

•  $\frac{\pi}{2}$  

•  $\frac{\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

Solve the trigonometric equation:

 $\tan^2\left(x\right)+2\tan\left(x\right)=-1$  

•  $\frac{\pi}{4},\frac{5\pi}{4}$  

•  $\frac{2\pi}{3},\frac{5\pi}{3}$  

•  $\frac{7\pi}{6},\frac{\pi}{6}$  

•  $\frac{3\pi}{4},\frac{7\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

Solve the trigonometric equation:

 $\sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right)$  

•  $\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\frac{2\pi}{3},\frac{5\pi}{3}$  

•  $\frac{\pi}{6},\frac{5\pi}{6}$  

•  $0,\pi$  

Tags

CCSS.HSF.TF.B.7

The value of  $\sin^{-1}\left(-\frac{1}{2}\right)\$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{3}$  

•  $-\frac{\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$  is

•  $\frac{5\pi}{6}$  

•  $-\frac{5\pi}{6}$  

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

csc^-1(-√(2))

• π/4
• 3π/4
• -π/4
• -3π/4

Tags

CCSS.HSF.TF.B.7