Free Printable Review Trigonometry

1.

Simplify the trigonometric identity $\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}$

a)

$\frac{2}{\cos x}$

b)

$\frac{2}{\sin x}$

c)

$\frac{2}{\tan x}$

2.

The equation $5\left(2\sin x-\cos x\right)=4\left(\sin x+2\cos x\right)$ when $\cos x\ne0$ can be written as ....

a)

$\tan x=\frac{11}{5}$

b)

$\tan x=\frac{5}{6}$

c)

$\tan x=\frac{13}{6}$

3.

By changing the expression in terms of $\cos x$ , solve the equation $\sin x\tan x=3\cos x$

for $0^0\le x\le360^0$

a)

30⁰, 150⁰, 210⁰, 330⁰

b)

60⁰, 120⁰, 240⁰, 300⁰

c)

60⁰, 120⁰, 210⁰, 300⁰

4.

Solve $4\sin^2x=7-8\cos x$ for $0\le x\le2\pi$

a)

$\frac{\pi}{6},\ \frac{5\pi}{3}$

b)

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

c)

$\frac{\pi}{3},\frac{11\pi}{6}$

5.

Express $2\sin^2x-7\cos^2x+4$ in terms of $\sin x$

a)

$9\sin^2x-3$

b)

$9\sin^2x+3$

c)

$9\sin^2x-6$

6.

What is the exact value of $\sin30^0.\cos60^0$

a)

$\frac{1}{4}$

b)

$\frac{\sqrt[]{3}}{4}$

c)

$\frac{\sqrt[]{3}}{2}$

7.

Given that $\tan\theta=\frac{2}{\sqrt[]{5}}$ and $\theta$ is an acute angle.

What is the exact value of $\sin\theta$

a)

$\frac{2}{\sqrt[]{5}}$

b)

$\frac{2}{3}$

c)

$\frac{\sqrt[]{5}}{3}$

8.

Simplify $\frac{\tan^2x\cos^2x}{\sin x}$

a)

$\sin x$

b)

$\cos x$

c)

$\tan x$

9.

The diagram shows the angle $\theta=-515^0$

Find the basic angle of $\theta$

a)

-65⁰

b)

65⁰

c)

25⁰

10.

Given $\theta$ is an angle which lies in the third quadrant where 0≤ $\theta$ ≤ $2\pi$ and its basic angle is $\frac{\pi}{4}$

Find the value of $\theta$

a)

$\frac{\pi}{4}$

b)

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

c)

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

11.

Given that $\sin\theta=\frac{1}{\sqrt[]{3}}$ and that θ is obtuse,

find the value of $\cos\theta$

a)

$-\frac{\sqrt[]{2}}{3}$

b)

$-\frac{\sqrt[]{6}}{3}$

c)

$\frac{\sqrt[]{6}}{\sqrt[]{3}}$

12.

Given that $\sin A=-\frac{5}{13}$ and $\cos B=\frac{4}{5}$ , where A and B are in the same quadrant.

Find the value of $\cos A.\tan B$

a)

$-\frac{9}{13}$

b)

$-\frac{16}{13}$

c)

$\frac{9}{13}$

13.

Which of the functions below represents the graph below?

a)

y = -cos 2x

b)

y = cos 2x

c)

y = -cos x

14.

Which of the trigonometric functions correspond to the graph shown below?

a)

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

b)

$y=2\sin4x$

c)

$y=2\cos\ \frac{x}{4}$

15.

The function $f\left(x\right)=2\cos\ \frac{x}{3}$ is defined for the domain $0\le x\le3\pi$

What is the inverse of $f\left(x\right)$

a)

$f^{-1}\left(x\right)=3\cos^{-1}\left(\frac{x}{2}\right)$

b)

$f^{-1}\left(x\right)=3\cos^{-1}\left(2x\right)$

c)

$f^{-1}\left(x\right)=2\cos^{-1}\left(3x\right)$

16.

What are the solution of $3\cos\left(2x\right)+1=0$ for $0^0\le x\le180^0$

a)

$\left\{109.47^0,\ 250.53^0\right\}$

b)

$\left\{70.53^0,\ 289.47^0\right\}$

c)

$\left\{54.74^0,\ 125.27^0\right\}$

17.

Which of the following is the graph of $y=\sin^{-1}x$

a)

b)

c)

d)

18.

Look at the following graph.

What is periode of graph of the trigonometric function above?

a)

180⁰

b)

-180⁰

c)

360⁰

19.

What is amplitude of $y=-3\cos\left(x+2\right)$

a)

1

b)

2

c)

3

20.

Let $\cos50^0=t$ then $\sin130^0$

a)

$\sqrt[]{1+t^2}$

b)

$\sqrt[]{1-t^2}$

c)

$\frac{1}{\sqrt[]{1-t^2}}$

Review Trigonometry

Total questions: 20

Worksheet time: 17mins

Similar Resources on Wayground