Free Printable Trigonometric Functions

1.

What is the sign of the function

\sin100

a)

negative

b)

0

c)

positive

d)

undefined

2.

Which expression is equivalent to the trigonometric expression $\frac{\cos^2\left(\theta\right)-1}{\sin^2\left(\theta\right)-1}$ ?

a)

$\cot^{2\ }\left(\theta\right)$

b)

$\tan^{2\ }\left(\theta\right)$

c)

$-\cot^{2\ }\left(\theta\right)$

d)

$-\tan^{2\ }\left(\theta\right)$

3.

Which expression is equivalent to the trigonometric expression $\cot\left(\theta\right)\cdot\sec\left(\theta\right)$ ?

a)

$\sec\left(\theta\right)$

b)

$1$

c)

$\csc\left(\theta\right)$

d)

$\tan\left(\theta\right)$

4.

Which identity represents a double-angle identity for sin 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

5.

Please choose the correct sum and difference formula:
sin (α-β) =

a)

sin α cos β + cos α sin β

b)

sin α cos β - cos α sin β

c)

cos α cos β - sin α sin β

d)

cos α cos β + sin α sin β

6.

sin 105 $\degree$ =

a)

$\frac{\left(\sqrt{3}+1\right)}{2\sqrt{2}}$

b)

$\frac{\left(\sqrt{3}-1\right)}{2\sqrt{2}}$

c)

$\frac{\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)}$

d)

none of the above

7.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

8.

cos (180° + x) =

a)

cosx

b)

sinx

c)

-sinx

d)

-cosx

9.

Which expression is equivalent to the trigonometric expression $\frac{1}{\left(1-\cos\left(\theta\right)\right)\cdot\left(1+\cos\left(\theta\right)\right)}$ ?

a)

$\sin^2\left(\theta\right)$

b)

$\cos^2\left(\theta\right)$

c)

$\sec^2\left(\theta\right)$

d)

$\csc^2\left(\theta\right)$

10.

Which expression is equivalent to the trigonometric expression $\frac{\tan\left(\theta\right)}{\sin\left(\theta\right)}$ ?

a)

$\cot\left(\theta\right)$

b)

$\sec\left(\theta\right)$

c)

$\cos\left(\theta\right)$

d)

$\csc\left(\theta\right)$

11.

Which expression is equivalent to the trigonometric expression $\frac{1-\sin^2\left(\theta\right)}{\cos\left(\theta\right)}$ ?

a)

$\sec\left(\theta\right)$

b)

$\sin\left(\theta\right)$

c)

$\cos\left(\theta\right)$

d)

$\csc\left(\theta\right)$

12.

$\frac{\tan\left(\frac{3\pi}{2}-x\right).\cot\left(\frac{\pi}{2}+x\right)+\sin^2\left(\frac{\pi}{2}-x\right)}{1-\cos\left(\pi+x\right)}$

a)

$-1-\cos x$

b)

$1-\cos x$

c)

$1-\sin x$

d)

$\cos x-1$

e)

$1+\sin x$

13.

$\tan\left(\frac{3\pi}{2}+x\right)=?$

a)

$-\tan x$

b)

$\cot x$

c)

$\tan x$

d)

$-\cot x$

14.

$\tan\left(\frac{3\pi}{2}-x\right)=?$

a)

$-\tan x$

b)

$\cot x$

c)

$\tan x$

d)

$-\cot x$

15.

$\cos\left(\frac{3\pi}{2}+x\right)=?$

a)

$-\sin x$

b)

$\cos x$

c)

$\sin x$

d)

$-\cos x$

16.

$\sin\left(\frac{\pi}{2}+x\right)=?$

a)

$-\sin x$

b)

$\cos x$

c)

$\sin x$

d)

$-\cos x$

17.

$\sin\left(\pi-x\right)=?$

a)

$-\sin x$

b)

$\cos x$

c)

$\sin x$

d)

$-\cos x$

18.

Which of the following is true?

(there are more than one answer)

a)

$\sin x=\frac{1}{\operatorname{cosec}x}$

b)

$\cot x.\tan x=1$

c)

$\sec x.\cot x=\cos x$

d)

$\sin^2x-\cos^2x=-1$

e)

$\operatorname{cosec}^2x+\sec^2x=\sec^2x.\operatorname{cosec}^2x$

19.

What is the sign of the function

\cos300

a)

negative

b)

0

c)

positive

d)

undefined

20.

What is the sign of the function

\operatorname{cosec}250

a)

negative

b)

0

c)

positive

d)

undefined

21.

What is the sign of the function

\sin160

a)

negative

b)

0

c)

positive

d)

undefined

22.

What is the sign of the function

\cot80

a)

negative

b)

0

c)

positive

d)

undefined

23.

What is the sign of the function

\sec280

a)

negative

b)

0

c)

positive

d)

undefined

24.

What is the sign of the function

\tan310

a)

negative

b)

0

c)

positive

d)

undefined

25.

What is the sign of the function

\cot190

a)

negative

b)

0

c)

positive

d)

undefined

26.

What is the sign of the function

\cos220

a)

negative

b)

0

c)

positive

d)

undefined

27.

What is the sign of the function

\tan253

a)

negative

b)

0

c)

positive

d)

undefined

Trigonometric Functions

Total questions: 27

Worksheet time: 28mins

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