Inverses and Solving Trig Equations

 $\cos^{-1}\left(1\right)=$  

• 0

• 1

•  $\pi$  

•  $\frac{\pi}{2}$  

Tags

CCSS.HSF.TF.B.7

 $\csc^{-1}\left(2\right)=$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{2}$  

Tags

CCSS.HSF.TF.B.7

 $\cos\left(\arctan\ \frac{3}{4}\right)=$  

•  $1$  

•  $\frac{3}{4}$  

•  $\frac{3}{5}$  

•  $\frac{4}{5}$  

Use a calculator:

 $\cos^{-1}\left(-0.81\right)=$  

•  $21.12\degree$  

•  $123.87\degree$  

•  $35.90\degree$  

•  $144.10\degree$  

Tags

CCSS.HSF.TF.B.7

Find ALL solutions to the following:

 $\sin x=-\frac{\sqrt{2}}{2}$  

•  $\frac{5\pi}{4}+n\pi$  

•  $\frac{5\pi}{4}+2n\pi\ ,\ \frac{7\pi}{4}+2n\pi$  

•  $\frac{7\pi}{4}+n\pi$  

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

Tags

CCSS.HSF.TF.B.7

Select all solutions that are within the interval

 $\left[0,2\pi\right)$  .

 $\tan\left(x+\frac{\pi}{6}\right)+1=0$  

•  $-\frac{5\pi}{12}$  

•  $\frac{7\pi}{12}$  

•  $\frac{5\pi}{12}$  

•  $\frac{11\pi}{12}$  

•  $\frac{19\pi}{12}$  

Tags

CCSS.HSF.TF.B.7

Select all solutions within the interval  $\left[0,2\pi\right)$  .

 $\sin\ \frac{x}{2}=\frac{\sqrt{3}}{2}$  

•  $\frac{2\pi}{3}$  

•  $\frac{\pi}{3}$  

•  $\frac{4\pi}{3}$  

•  $\frac{5\pi}{3}$  

•  $\frac{17\pi}{3}$  

Tags

CCSS.HSF.TF.B.7

The rabbit population of an area is described by  $N\left(t\right)=2400+500\sin\left(\pi t\right)$  , where N(t) gives the number of rabbits in the area after t years. When will the rabbit population first reach 1900?

Fill your decimal answer into the blank.

_______ years

Tags

CCSS.HSF.TF.B.7