Free Printable Trig Ratios and Identities

1.

What can be entered into a calculator in order to solve for x:

\tan12\degree\ =\ \frac{22}{x}

a)

$\frac{22}{\tan\left(12\degree\right)}$

b)

22 tan(12)

c)

103.5

d)

none of these

2.

Which of these are correct ratios for the given triangle?

a)

$\sin40\degree\ =\ \frac{w}{28}$

b)

$\cos50\degree=\ \frac{w}{28}$

c)

$\sin40=\frac{28}{w}$

d)

$\cos50\degree=\frac{28}{w}$

3.

Susan is flying a kite, which gets caught in the top of a tree. Which equation can be used to find the height of the tree?

a)

$\sin\ 44\degree=\frac{x}{90}$

b)

$\cos44\degree=\frac{x}{90}$

c)

$\tan40\degree=\frac{x}{90}$

d)

$x^2+90^2=44^2$

4.

Find x.

a)

10

b)

√3

c)

5

d)

10√3

5.

Please select the correct solution
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

6.

Please select the correct solution

a)

csc x

b)

sec x

c)

cot x

d)

tan x

7.

True or false:
sin²θ = (sin θ)²

a)

True

b)

False

8.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

9.

*

a)

cos x

b)

csc x

c)

sec x

d)

cot x

10.

*

a)

sin x

b)

cos x

c)

tan x

d)

csc x

11.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

12.

secant is the reciprocal of

a)

sine

b)

cosine

c)

tangent

d)

cosecant

13.

csc x is the same as

a)

$\frac{1}{\sin x}$

b)

$\frac{1}{\tan x}$

c)

$\sin\ x$

d)

$\frac{1}{\cos x}$

14.

What is the length of y?

a)

8√2

b)

4√2

c)

4

d)

8

15.

sec x is the same as

a)

$\frac{1}{\sin x}$

b)

$\frac{1}{\tan x}$

c)

$\sin\ x$

d)

$\frac{1}{\cos x}$

16.

$\frac{\sin x}{\cos x}$ and $\frac{\cos\ x}{\sin x}$ are ______________ of each other

a)

opposites

b)

reciprocals

c)

inverses

d)

cousins

17.

Choose the true statements

a)

$\tan\theta=\frac{\sin\theta}{\cos\theta}$

b)

$\cos\theta\ =\ \frac{1}{\sin\theta}$

c)

$\cot\ \theta=\frac{\sin\theta}{\cos\theta}$

d)

$\cot\theta=\frac{\cos\theta}{\sin\theta}$

e)

$\sec\theta=\frac{1}{\cos\theta}$

18.

Which ones are the Quotient Identities?

a)

$\frac{\sin\theta}{\cos\theta}=\tan\theta$

b)

$\frac{1}{\sin\theta}=\csc\theta$

c)

$\frac{1}{\cos\theta}=\sec\theta$

d)

$\cot\theta=\frac{\cos\theta}{\sin\theta}$

e)

$\cot\theta=\frac{1}{\tan\theta}$

19.

Which ones are the Reciprocal Identities?

a)

$\frac{\sin\theta}{\cos\theta}=\tan\theta$

b)

$\frac{1}{\sin\theta}=\csc\theta$

c)

$\frac{1}{\cos\theta}=\sec\theta$

d)

$\cot\theta=\frac{\cos\theta}{\sin\theta}$

e)

$\cot\theta=\frac{1}{\tan\theta}$

20.

Fill in the blank:

\cot x\ =\ \frac{?}{\sin x}

a)

sin(x)

b)

cos(x)

c)

tan(x)

d)

csc(x)

21.

Which of the following is NOT a pythagorean identity?

a)

sin²x + cos²x = 1

b)

1 - cos²x = sin²x

c)

1 - sin²x = cos² x

d)

sin²x - cos²x = -1

22.

What can be entered into a calculator in order to solve the equation

\sin38\degree=\frac{x}{16}

a)

9.9

b)

16 sin(38)

c)

$\frac{\sin38}{16}$

d)

16 csc(38)

23.

What is the length of x?

a)

4√2

b)

4

c)

8

d)

4√3

24.

Check all correct equations

a)

$\sin\ 40\degree=\frac{x}{19}$

b)

$\cos50\degree=\frac{x}{19}$

c)

$\sec40\degree=\frac{19}{x}$

d)

$\csc40\degree=\frac{19}{x}$

Trig Ratios and Identities

Total questions: 24

Worksheet time: 37mins

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