Solving Trig Equations IV

If you were given the equation  $\cos\theta=-\frac{1}{2}$ , which variable in the ordered pairs on the unit circle would you look at to find your answer?

• x

• y

• None of the above

• Both x and y

Tags

CCSS.HSF.TF.A.2

If you were given the equation

 $\sin\theta=-\frac{\sqrt{2}}{2}$  and you looked on your unit circle to find possible answers, in which two quadrants would you find them?

• I and II

• II and III

• III and IV

• IV and I

Tags

CCSS.HSF.TF.B.7

 $\sin^2\theta=2\cos\theta+2$  Which identity would you have to use to solve the following equation?

•  $\cos\left(2\theta\right)=\cos^2\theta-\sin^2\theta$  

•  $\sin\left(2\theta\right)=2\sin\theta\cos\theta$  

•  $\sin^2\theta=1-\cos^2\theta$  

•  $\cos^2\theta=1-\sin^2\theta$  

Tags

CCSS.HSF.TF.C.8

If you were given the equation $2\cos^2\theta+3\cos\theta+1=0$  and you likened it to the equation  $2x^2+3x+1=0$  , what would its factored form be?

•  $\left(2x+3\right)\left(x+1\right)$  

•  $\left(2x+1\right)\left(x+1\right)$  

•  $\left(x+1\right)\left(x+1\right)$  

•  $\left(3x+1\right)\left(x+1\right)$  

Tags

CCSS.HSA-REI.B.4B

Solve equation for  $0\le\theta<2\pi$  .
 $-2+\cot\theta=-3$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $4+\csc^2\theta=2\csc^2\theta$  

•  $\theta=\frac{5\pi}{6},\frac{4\pi}{3}$  

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

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

•  $\theta=\frac{\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$  

•  $\theta=\frac{5\pi}{4},\frac{11\pi}{6}$  

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

•  $\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\theta=\frac{5\pi}{4},\frac{7\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

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

•  $\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$  

•  $\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$  

•  $\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\theta=0,\pi,\frac{5\pi}{3}$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $\sec^2\theta+3=2\sec\theta+2$  

•  $\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$  

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

•  $\theta=\frac{\pi}{4}$  

•  $\theta=0$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$  

•  $\theta=\frac{7\pi}{6}$  

•  $\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$  

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

•  $\theta=\frac{7\pi}{6},\frac{11\pi}{6}$  

Tags

CCSS.HSF.TF.B.7