Free Printable Trig Identities and Solving Trig Equations

1.

Which of these are equal to 1? (Check all that apply)

a)

sin²(θ) + cos²(θ)

b)

sec²(θ) - tan²(θ)

c)

csc²(θ) - cot²(θ)

d)

tan²(θ) - cos²(θ)

2.

Which of these is false?

a)

$\cos\left(\frac{\pi}{2}-\theta\right)=\sin\left(\theta\right)$

b)

$\sin\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$

c)

$\sec\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$

d)

$\tan\left(\frac{\pi}{2}-\theta\right)=\cot\left(\theta\right)$

3.

Each trig function has a "cofunction" (Ex: sine and cosine are cofunctions).

How are cofunctions related to each other? (Check all that apply)

a)

Cofunctions of complementary angles are equal.

b)

Cofunctions are reciprocals of each other.

c)

Cofunctions are inverses of each other.

d)

Cofunctions are negatives of each other.

4.

$\frac{\tan\left(\theta\right)}{\cot\left(\theta\right)}\equiv$

a)

$1$

b)

$\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

c)

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

d)

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

5.

Solve for x:
$2\cos^2\left(x\right)+\cos\left(x\right)-1=0$
Check all possible answers

a)

x = 0

b)

x = $-\frac{\pi}{3}$

c)

x = $\pi$

d)

x = $\frac{\pi}{3}$

e)

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

6.

Find $\sin\theta$ if $\cos\theta=\frac{3}{5}$ .

a)

$0.80$

b)

$0.63$

c)

$1.25$

d)

$1.58$

7.

Find $\sin\theta$ if $\tan\theta=12$ .

a)

$1.003$

b)

$0.997$

c)

$1.041$

d)

$0.961$

8.

If $\tan\theta=\frac{8}{4}$ , find $\cos\theta$ .

a)

$2.24$

b)

$0.45$

c)

$1.73$

d)

$0.58$

9.

If $\tan\theta=\frac{5}{3}$ , find $\sec\theta$ .

a)

$0.65$

b)

$1.63$

c)

$1.94$

d)

$0.94$

10.

If $\sec\theta=-2$ , find $\cos\theta$ .

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$2$

d)

$-\frac{1}{4}$

11.

TRUE or FALSE:
There is NO SOLUTION to sinθ = -1.

a)

TRUE

b)

FALSE

12.

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

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

13.

Which identity does not represent a double-angle identity for cos 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

14.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

15.

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

16.

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

17.

Solve on the interval [0,360)
2cosx-1=0

a)

60,120

b)

60, 240

c)

120, 240

d)

60, 300

18.

Solve for the unknown variable on the interval 0≤θ<2π

4cos²x - 3 = 0

a)

π/6, 5π/6

b)

π/6, 11π/6

c)

5π/6, 11π/6

19.

Solve: 2cscθ + 2 = 0

State all solutions in the interval [0, 2π)

a)

π/2, 3π/2

b)

π/2

c)

3π /2

d)

π

20.

Solve: 2cosx - 4 = 0

State all solutions in the interval [0, 2π)

a)

No solution

b)

π/3, 5π/3

c)

π/6, 11π/6

d)

2π/3, 4π/3

21.

Simplify: $\frac{\cos^2\left(-x\right)\csc x}{\cot x}$

a)

$-\sin x$

b)

$-\cos x$

c)

$\sin x$

d)

$\cos x$

22.

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

a)

$\cot^2x$

b)

$\tan^2x$

c)

$\csc^2x$

d)

$\sec^2x$

23.

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

a)

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

b)

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

c)

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

24.

Simplify: $\sec x-\tan x\sin x$

a)

$\sin x$

b)

$\cos x$

c)

$\csc x$

d)

$\sec x$

25.

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

26.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

Trig Identities and Solving Trig Equations

Total questions: 26

Worksheet time: 1hrs 12mins

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