Free Printable Practice with the Trig Identities

1.

a)

sec(u)

b)

cos(u)

c)

tan(u)

d)

sin(u)

e)

cot(u)

2.

cos(-u)

a)

cos(u)

b)

-cos(u)

c)

sin(u)

d)

-sec(u)

e)

sec(u)

3.

Select all that are Pythagorean Identities.

a)

sin²(u) + cos²(u) = 1

b)

sin²(u) - cos²(u) = 1

c)

tan²(u) + 1 = sec²(u)

d)

cot²(u) + csc²(u) = 1

e)

cot²(u) + 1 = csc²(u)

4.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

5.

Simplify

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

6.

Which could be a first strategy to simplify the left side?

a)

Rewrite into sines and cosines

b)

Combine fractions

c)

Factor common factor (GCF)

d)

Distribute

e)

Combine like terms (add or subtract)

7.

What could be our first strategy to simplify the right side?

a)

Rewrite into sines and cosines

b)

Combine fractions

c)

Factor common factor (GCF)

d)

Distribute

e)

Use a Pythagorean Identity

8.

Simplify to a single trig expression

a)

$-\cos x$

b)

$\cos x$

c)

1

d)

$\tan^2x$

e)

$\sin x$

9.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

10.

Which of the following is equivalent to $\tan\ \left(A-B\right)$

a)

$\tan\ A\ -\ \tan\ B$

b)

$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$

c)

$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$

d)

$\frac{\sin\ A}{\cos\ B}$

11.

Please choose the correct sum and difference formula:
cos (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

12.

If $\cos A=\frac{3}{5}$ where $0\degree\le A\le90\degree$ and $\sin B=\frac{5}{13}$ where $90\degree\le B\le180\degree$ find $\cos\left(A+B\right)$ .

(No Decimals accepted!)

(a)

13.

$If\ \sin\theta\ =\ \frac{4}{5},\ where\ 0\le\theta\le\frac{\pi}{2},find\ \sin2\theta$

a)

$\frac{12}{25}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$\frac{3}{5}$

14.

$If\ \sin\theta\ =\ \frac{-4}{5},\ where\ \pi\le\theta\le\frac{3\pi}{2},find\ \sin2\theta$

a)

$\frac{12}{25}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$\frac{3}{5}$

15.

$If\ \sin\theta\ =\ \frac{-4}{5},\ where\ \pi\le\theta\le\frac{3\pi}{2},find\ \tan2\theta$

a)

$\frac{-24}{7}$

b)

$\frac{24}{7}$

c)

$-\frac{24}{25}$

d)

$\frac{24}{25}$

16.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

17.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

18.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

19.

Why doesn't 2cosx − 3 = 0 have solutions?

a)

cos x is never bigger than one

b)

cos x is never equal to a fraction

c)

Actually, this equation does have a solution, x = π

d)

This equation will have a solution tomorrow.

20.

$\tan x=\tan x\sin x$

a)

$x=0,\ \frac{\pi}{2},\ \pi$

b)

$x=0,\ \pi$

c)

$x=0,\ \frac{\pi}{2}$

d)

No solution.

21.

$2\cos^2x=3\cos x-1$

a)

$x=0,\ \frac{\pi}{6},\ \frac{11\pi}{6}$

b)

$x=0,\ \frac{\pi}{3},\ \pi,\ \frac{5\pi}{3}$

c)

$x=0,\ \frac{\pi}{3},\ \frac{5\pi}{3}$

d)

$x=\frac{2\pi}{3},\ \pi,\ \frac{4\pi}{3}$

22.

Solve: $5\tan x+3=6\tan x+4;\ \left[0,\ \pi\right]$

a)

-1

b)

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

c)

$\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\frac{\pi}{4},\frac{3\pi}{4},\ \frac{5\pi}{4},\frac{7\pi}{4}$

23.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers. $\tan\theta=-\sqrt{3}$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

24.

Simplify: $\frac{1-\cos2x}{2}$

a)

$-\sin^2x$

b)

$\sin^2x$

c)

$0$

d)

$\cos^2x$

25.

Solve over the interval [ $0,\ 2\pi$ ) : $\sin2x+\sin x=0$

a)

$0,\ \frac{2\pi}{3},\ \pi,\ \frac{4\pi}{3}$

b)

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

c)

$0,\ \frac{\pi}{3},\ \pi,\ \frac{5\pi}{3}$

d)

$\frac{\pi}{2},\ \frac{\pi}{3},\ \frac{3\pi}{2},\ \frac{5\pi}{3}$

26.

$2\sin\left(3x\right)\cos\left(3x\right)=$

a)

$\sin\left(6x\right)$

b)

$\sin\left(6x\right)\cos\left(6x\right)$

c)

$\cos\left(6x\right)$

d)

$\sin\left(3x\right)$

Practice with the Trig Identities

Total questions: 26

Worksheet time: 4hrs 25mins

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