Free Printable Trig Identities: Pythagorean, Sum/Diff, Double, Half-Angle

1.

sin(x) =

a)

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

b)

$\frac{1}{\csc\ x}$

c)

$\frac{1}{\sec\ x}$

d)

$\csc\ x$

2.

$1-\cos^2x\$

a)

$\tan^2x$

b)

$\cos\ 2x$

c)

$\sin^2x$

d)

$\sin\ 2x$

3.

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

a)

cos x

b)

sin x

c)

sin 2x

d)

sinx cosx

4.

$\cos\left(x+\pi\right)=\$

a)

sin x

b)

cos x

c)

-sin x

d)

-cos x

5.

Which of the follow is NOT a way to simplify the following: $\tan^2x\ -\tan^2x\csc^2x$

a)

$\tan^2x\left(1-\csc^22x\right)$

b)

$\frac{\sin^2x}{\cos^2x}-\ \frac{\sin^2x}{\cos^2x}\cdot\frac{1}{\sin^2x}$

c)

$\left(\tan x-\csc x\right)\cdot\left(\tan x+\csc x\right)$

d)

$\tan^2x\left(\cot^2x\right)$

6.

Which of the following is NOT equivalent to $\frac{2\cos^2x}{\tan^2x}$

a)

$\left(2-2\sin^2x\right)\left(\frac{1}{\cot^2x}\right)$

b)

$\left(2\cos^2x\right)\left(\frac{\sin^2x}{\cos^2x}\right)$

c)

$\sin^22x\left(\cot^2x\right)$

d)

$\frac{2\cos^2x}{\sec^2x-1}$

7.

Which of the following is Not equivalent to: $2\cos^2x-1$

a)

$\sin^2x$

b)

$2\cos^2x-\left(\sin^2x+\cos^2x\right)$

c)

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

d)

$\sin^22x$

8.

Given:

\sin\ x=\frac{-3}{5}\ and\ \pi<x<\frac{3\pi}{2},

find cos (2x).

a)

$\frac{12}{25}$

b)

$-\frac{7}{25}$

c)

$\frac{7}{25}$

d)

$\frac{3\sqrt{10}}{10}$

9.

Simplfy

\sin\left(70\right)\cos\left(20\right)+\cos\left(70\right)\sin\left(20\right)

a)

cos (90)

b)

sin (90)

c)

cos(50)

d)

sin (50)

10.

Simplify: cos(40)cos(50) - sin(40)sin(50).

a)

sin (10)

b)

cos (10)

c)

sin (90)

d)

cos (90)

11.

Simplify and evaluate:

sin(150)cos(30) - cos(150)sin(30).

a)

1

b)

0

c)

$\frac{1}{2}$

d)

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

12.

Using Sum and Difference,

\cos\ \left(\frac{5\pi}{12}\right)\

can be written several ways. Which of the following is NOT one of those ways.

a)

$\cos\left(\frac{\pi}{6}+\frac{\pi}{4}\right)$

b)

$\cos\left(\frac{2\pi}{3}-\frac{\pi}{4}\right)$

c)

$\cos\left(\frac{2\pi}{3}+\frac{\pi}{4}\right)$

d)

$\cos\left(\frac{5\pi}{4}-\frac{5\pi}{6}\right)$

13.

Using the half-angle rule, rewrite:

\sin\left(\frac{7\pi}{8}\right)

a)

$\sin\left(\frac{7\pi}{4}\right)$

b)

$\sin\left(\frac{1}{2}\cdot\frac{7\pi}{4}\right)$

c)

$\sin\left(\frac{1}{2}\cdot\frac{7\pi}{8}\right)$

d)

$\sin\left(\frac{1}{2}\cdot\frac{7\pi}{16}\right)$

Trig Identities: Pythagorean, Sum/Diff, Double, Half-Angle

Total questions: 13

Worksheet time: 7mins

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