Free Printable Inverses and Solving Trig Equations

1.

$\cos^{-1}\left(1\right)=$

a)

0

b)

1

c)

$\pi$

d)

$\frac{\pi}{2}$

2.

$\csc^{-1}\left(2\right)=$

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{2}$

3.

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

a)

$1$

b)

$\frac{3}{4}$

c)

$\frac{3}{5}$

d)

$\frac{4}{5}$

4.

Use a calculator:

\cos^{-1}\left(-0.81\right)=

a)

$21.12\degree$

b)

$123.87\degree$

c)

$35.90\degree$

d)

$144.10\degree$

5.

Find ALL solutions to the following:

\sin x=-\frac{\sqrt{2}}{2}

a)

$\frac{5\pi}{4}+n\pi$

b)

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

c)

$\frac{7\pi}{4}+n\pi$

d)

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

6.

Select all solutions that are within the interval

\left[0,2\pi\right)

.

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

a)

$-\frac{5\pi}{12}$

b)

$\frac{7\pi}{12}$

c)

$\frac{5\pi}{12}$

d)

$\frac{11\pi}{12}$

e)

$\frac{19\pi}{12}$

7.

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

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

a)

$\frac{2\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$\frac{4\pi}{3}$

d)

$\frac{5\pi}{3}$

e)

$\frac{17\pi}{3}$

8.

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.

(a) years

Inverses and Solving Trig Equations

Total questions: 8

Worksheet time: 15mins

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