Free Printable Unit 6 Review

1.

Solve the following for cos²θ:
sin²θ + cos²θ = 1

a)

cos²θ = 1 - sin²θ

b)

cosθ = 1 + sin²θ

c)

cosθ = 1 - sinθ

d)

cos²θ = Adj/hyp

2.

Solve the following for tan²θ:
1 + tan²θ = sec²θ

a)

tan²θ = sec²θ + 1

b)

tan²θ = sec²θ - 1

c)

tanθ = secθ - 1

d)

tan²θ = opp/adj

3.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

4.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

5.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

6.

Please select the correct solution cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

7.

Please select the correct solution

a)

csc x

b)

sec x

c)

cot x

d)

tan x

8.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

9.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

10.

Simplify

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

11.

sin x =

a)

cos x

b)

1/cosx

c)

1/secx

d)

1/cscx

12.

cos x =

a)

sin x

b)

sin²x-1

c)

1/sec x

d)

1/csc x

13.

sec x =

a)

1/cosx

b)

1/sinx

c)

1/cscx

d)

1/tanx

14.

csc x =

a)

1/cosx

b)

1/sinx

c)

cot²x-1

d)

1/secx

15.

cotx =

a)

sinx/cosx

b)

cosx/sinx

c)

1/tanx

d)

1/cotx

16.

Simplify

$\cot\theta\tan\theta$

a)

sin²θ/cos²θ

b)

1

c)

0

d)

cos²θ/sin²θ

17.

Simplify
$\sec\theta\cot\theta\sin\theta$

a)

-1

b)

sin θ

c)

csc θ

d)

1

18.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

19.

Simplify

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

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

20.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

21.

Simplify

$\cot\theta\sin\theta$

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

22.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

23.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

24.

Simplify $\tan x\left(\cot x\ +\ \csc x\right)$

a)

1 + sec x

b)

1 + csc x

c)

sec x - 1

d)

tan² x

25.

Simplify $\left(\csc x+1\right)\left(\csc x-1\right)$

a)

$\csc^2x+1$

b)

$\tan^2x$

c)

$\cot^2x$

d)

$2\csc x$

26.

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

27.

Simplify
(sec x)(cot x)(sin x)

a)

sin x

b)

- sin x

c)

1

d)

-1

28.

a)

1/cos x

b)

1

c)

cot x

d)

-1

29.

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

30.

a)

csc x

b)

sec x

c)

1/sec x

d)

cos x

31.

On the domain [0, 2π), solve this equation 0 = sinx(sinx − 1)

a)

0, π

b)

0, π, ½π

c)

½π

d)

0, 90, 270

32.

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)

33.

Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree

a)

$x\ =\ 60\degree,\ 120\degree$

b)

$x\ =\ 60\degree,\ 300\degree$

c)

$x\ =\ 30\degree,\ 150\degree$

d)

$x\ =\ 30\degree,\ 330\degree$

34.

$Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree$

a)

$30\degree,\ 210\degree$

b)

$150\degree,\ 330\degree$

c)

$60\degree,\ 240\degree$

d)

$120\degree,\ 300\degree$

35.

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)

$300\degree$

36.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$6\sin\theta=3$

a)

$60\degree$

b)

$300\degree$

c)

$30\degree$

d)

$150\degree$

37.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$4\cos\theta=-2$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

38.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$5+\tan\theta=4$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

39.

Find the exact value of the expression.
$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$-\frac{\sqrt{2}}{2}$

d)

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

40.

Use a sum or difference formula to find an exact value of sin 105º

a)

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

b)

$\frac{-\sqrt{2}-\sqrt{6}}{4}$

c)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

d)

$2-\sqrt{3}$

41.

Use Sum or Difference Identities to find the exact value of each expression.
cos(75°)

a)

1/4

b)

( √(6) - √(2) ) / 4

c)

(√(6) + √(2)) / 4

d)

(-√(6) - √(2)) / 4

42.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

43.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

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

44.

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)

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

45.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

46.

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

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

Unit 6 Review

Total questions: 46

Worksheet time: 12hrs 30mins

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