Free Printable PC: Chapter 5 Review

1.

Solve for 0≤x≤2π

2cos²x + cosx = 0

a)

π/2, 3π/2

b)

0, π,2π

c)

2π/3, 4π/3

d)

π/3, 5π/3

2.

Solve for 0≤x≤2π

4cos²x- 2 = 0

a)

π/3, 5π/3

b)

π/4, 7π/4

c)

3π/4, 5π/4

d)

π/6, 11π/6

3.

Solve for 0≤x≤2π

sinxtanx = sinx

a)

π/2, 3π/2

b)

3π/4, 7π/4

c)

0, π, 2π

d)

π/4, 5π/4

4.

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

a)

π/6, 5π/6

b)

7π/6, 11π/6

c)

π/3, 2π/3

d)

4π/3, 5π/3

5.

Solve for 0≤x≤2π

2sin²x - sinx = 0

a)

0, π, 2π

b)

π/2, 3π/2

c)

π/6, 5π/6

d)

π/3, 2π/3

6.

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0

a)

0, π

b)

π/2

c)

π/6, 5π/6

d)

3π/2

7.

Simplify

a)

cotx

b)

tanx

c)

cosx

d)

sinx

8.

Simplify

a)

secx

b)

cscx

c)

sinx

d)

cosx

9.

Simplify

a)

cosx

b)

sinx

c)

1

d)

tanx

10.

Simplify

a)

$\cos^2x$

b)

$\sec^2x$

c)

\tan^2x

d)

$\cot^2x$

11.

$Use\ the\ sum\ and\ difference\ formula\ to\ solve:\ \tan75\degree$

a)

$2+\sqrt{3}$

b)

$-2+\sqrt{3}$

c)

$-2-\sqrt{3}$

d)

$2-\sqrt{3}$

12.

$Use\ the\ sum\ or\ difference\ formula\ to\ find:\ \cos75\degree$

a)

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

b)

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

c)

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

d)

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

13.

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$15\degree$

a)

$75\degree-60\degree$

b)

$115\degree-100\degree$

c)

$60\degree-45\degree$

d)

$85\degree-70\degree$

14.

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$165\degree$

a)

$185\degree-20\degree$

b)

$45\degree+120\degree$

c)

$35\degree+130\degree$

d)

$180\degree-15\degree$

15.

Use a sum or difference identity to find the EXACT value:

$\sin\left(15\degree\right)$

a)

0.2588

b)

0.6503

c)

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

d)

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

16.

Use a sum or difference identity to find the EXACT value:

$\cos\left(105\degree\right)$

a)

-0.2410

b)

-0.2588

c)

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

d)

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

17.

Use a sum or difference identity to find the EXACT value:

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

a)

0.9659

b)

0.9999

c)

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

d)

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

18.

Write the expression as the sine or cosine of a single angle:

$\sin42\degree\cos17\degree-\cos42\degree\sin17\degree$

a)

$\sin\left(59\degree\right)$

b)

$\cos\left(59\degree\right)$

c)

$\sin\left(25\degree\right)$

d)

$\cos\left(25\degree\right)$

19.

Write the expression as the sine or cosine of a single angle:

$\cos94\degree\cos18\degree+\sin94\degree\sin18\degree$

a)

$\cos\left(76\degree\right)$

b)

$\sin\left(76\degree\right)$

c)

$\cos\left(112\degree\right)$

d)

$\sin\left(112\degree\right)$

20.

Write the expression as the sine or cosine of a single angle:

$\sin\left(\frac{\pi}{5}\right)\cos\left(\frac{\pi}{2}\right)+\sin\left(\frac{\pi}{2}\right)\cos\left(\frac{\pi}{5}\right)$

a)

$\cos\left(\frac{3\pi}{10}\right)$

b)

$\sin\left(\frac{3\pi}{10}\right)$

c)

$\cos\left(\frac{7\pi}{10}\right)$

d)

$\sin\left(\frac{7\pi}{10}\right)$

21.

Write the expression as the sine or cosine of a single angle:

$\sin\left(\frac{\pi}{3}\right)\cos\left(\frac{\pi}{7}\right)-\sin\left(\frac{\pi}{7}\right)\cos\left(\frac{\pi}{3}\right)$

a)

$\cos\left(\frac{4\pi}{21}\right)$

b)

$\sin\left(\frac{4\pi}{21}\right)$

c)

$\cos\left(\frac{10\pi}{21}\right)$

d)

$\sin\left(\frac{10\pi}{21}\right)$

22.

Write the expression as the sine or cosine of a single angle:

$\cos\left(\frac{\pi}{7}\right)\cos x+\sin\left(\frac{\pi}{7}\right)\sin x$

a)

$\cos\left(\frac{\pi}{7}-x\right)$

b)

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

c)

$\cos\left(\frac{\pi}{7}+x\right)$

d)

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

23.

Write the expression as the sine or cosine of a single angle:

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

a)

$\cos\left(2x\right)$

b)

$\sin\left(2x\right)$

c)

$\cos\left(4x\right)$

d)

$\sin\left(4x\right)$

24.

Write the expression as the sine or cosine of a single angle:

$\cos\left(7y\right)\cos\left(3y\right)-\sin\left(7y\right)\sin\left(3y\right)$

a)

$\cos\left(4y\right)$

b)

$\sin\left(4y\right)$

c)

$\cos\left(10y\right)$

d)

$\sin\left(10y\right)$

25.

Find the exact value using the Sum and Difference Identities.

$\tan\left(\frac{19\pi}{12}\right)$

a)

$-2-\sqrt{3}$

b)

$2+\sqrt{3}$

c)

$1+2\sqrt{3}$

d)

$-2+3\sqrt{3}$

26.

Condense into a single trigonometric expression, then find the exact value.

$\frac{\tan162\degree-\tan42\degree}{1+\tan162\degree\tan42\degree}$

a)

$-\sqrt{3}$

b)

$\sqrt{3}$

c)

$1$

d)

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

PC: Chapter 5 Review

Total questions: 26

Worksheet time: 2hrs 10mins

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