Free Printable BC PreCalc Final Review Sem. 2

1.

If the point (-2, 3) lies on the terminal side of an angle θ, find the value of cosθ

a)

$-\frac{2\sqrt{13}}{13}$

b)

$-\frac{\sqrt{13}}{2}$

c)

$-\frac{2\sqrt{5}}{5}$

d)

$-\frac{2}{3}$

2.

Find sec(θ) given that the terminal side of θ contains the point $\left(\sqrt{5},2\right)$ .

a)

$\frac{3\sqrt{5}}{5}$

b)

$\frac{3}{2}$

c)

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

d)

$-\frac{\sqrt{5}}{3}$

3.

Given that cos $\theta$ = 3/4 and sin $\theta$ < 0, find tan $\theta.$

a)

$-\frac{\sqrt{7}}{4}$

b)

$-\frac{\sqrt{7}}{3}$

c)

$\frac{5}{3}$

d)

$-\frac{5}{3}$

e)

$\frac{\sqrt{7}}{3}$

4.

What is $\sin\left(\frac{\pi}{6}\right)$ ?

a)

1

b)

1/2

c)

√3/2

d)

√2/2

5.

What is the $\cos\left(\frac{3\pi}{4}\right)$ ?

a)

√3/2

b)

-√3/2

c)

√2/2

d)

-√2/2

6.

What is $\tan\left(\frac{5\pi}{6}\right)$ ?

a)

√3

b)

-√3

c)

√3/3

d)

-√3/3

7.

Evaluate: csc(3π/4)

a)

√2/2

b)

-√2/2

c)

√2

d)

-√2

8.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

9.

cot π/2

a)

undefined

b)

0

c)

1

d)

1/2

10.

What is $\sec\left(\frac{7\pi}{4}\right)$ ?

a)

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

b)

$\sqrt{2}$

c)

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

d)

$-\sqrt{2}$

11.

Find the sin(-9π/4)

a)

-√3/2

b)

-1/2

c)

√2/2

d)

-√2/2

12.

Find the period of $y=\cos\left(3\theta+π/2\right)$

a)

2π/3

b)

6π

c)

3π

d)

4π/3

13.

Find the phase shift of $y=\cos\left(3\theta+π/2\right)$

a)

- π/6

b)

π/6

c)

3π/2

d)

- 3π/2

14.

What is the equation of the asymptote for the following equation?

$y=\sec\left(\frac{1}{2}x\right)$

a)

$x=\frac{\pi}{2}+n\pi$

b)

$x=n\pi$

c)

$x=\frac{\pi}{4}+\frac{n\pi}{2}$

d)

$x=\pi+2n\pi$

e)

$x=\frac{n\pi}{2}$

15.

What is the equation of the asymptote for the following equation?

$y=2\csc\left(x\right)-1$

a)

$x=\frac{\pi}{2}+n\pi$

b)

$x=n\pi$

c)

$x=\frac{\pi}{4}+\frac{n\pi}{2}$

d)

$x=2n\pi$

e)

$x=\frac{n\pi}{2}$

16.

What is the equation of the asymptote for the following equation?

$y=2\tan\left(x\right)-1$

a)

$x=\frac{\pi}{2}+n\pi$

b)

$x=n\pi$

c)

$x=\frac{\pi}{4}+\frac{n\pi}{2}$

d)

$x=2n\pi$

e)

$x=\frac{n\pi}{2}$

17.

What is the equation of the asymptote for the following equation?

$y=\cot\left(2x-\frac{\pi}{2}\right)$

a)

$x=\frac{\pi}{2}+n\pi$

b)

$x=n\pi$

c)

$x=\frac{\pi}{4}+\frac{n\pi}{2}$

d)

$x=2n\pi$

e)

$x=\frac{n\pi}{2}$

18.

Which is a correct equation for the graph shown?

a)

$y=\frac{1}{2}\cos\left(2x\right)-3$

b)

$y=\frac{1}{2}\cos\left(\frac{1}{2}x\right)-3$

c)

$y=\frac{1}{2}\cos\left(2x+3\right)$

d)

$y=\frac{1}{2}\sin\left(2x\right)-3$

19.

Which is a correct equation for the graph shown?

a)

$y=-2\cos\left(\frac{\pi}{2}x\right)$

b)

$y=2\cos\left(\frac{\pi}{2}x\right)$

c)

$y=-2\sin\left(2\pi x\right)$

d)

$y=-2\cos\left(2\pi x\right)$

20.

Determine an equation for this graph:

a)

y=2csc(x)

b)

y=csc(x) + 1

c)

y=2csc(x) + 1

d)

y= csc(x) + 2

21.

Solve equation on $0\le\theta<2\pi$

$-2+\cot\theta=-3$

a)

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

b)

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

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

22.

Solve equation on $0\le\theta<2\pi$ .

$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

23.

Solve equation on $0\le\theta<2\pi$ .

$3\sin^2\theta+4=5+\sin^2\theta$

a)

$\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4}$

d)

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

24.

Solve equation for $0\le\theta<2\pi$ . $-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{5\pi}{4},\frac{7\pi}{4}$

25.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

26.

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

sinx + sin2x = 0

a)

2π/3, 4π/3, 0, π

b)

2π/3, 4π/3

c)

0, π

d)

π/3, 5π/3

27.

Simplify (Hint: Foil!!!)

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

28.

Simplify: $\tan\left(x\right)\cot\left(x\right)-\cos^2\left(x\right)$

a)

tanx

b)

cotx

c)

sin²x

d)

cos²x

29.

a)

-1

b)

sin θ

c)

csc θ

d)

1

30.

$\sin\ \left(\alpha\ +\ \beta\right)$

a)

$\left(\sin\ \alpha\right)\left(\cos\ \beta\right)\ -\ \left(\cos\ \alpha\right)\left(\sin\ \beta\right)$

b)

$\left(\sin\ \alpha\right)\left(\cos\ \beta\right)\ +\ \left(\cos\ \alpha\right)\left(\sin\ \beta\right)$

c)

$\left(\cos\ \alpha\right)\left(\cos\ \beta\right)\ -\ \left(\sin\ \alpha\right)\left(\sin\ \beta\right)$

d)

$\left(\cos\ \alpha\right)\left(\cos\ \beta\right)\ +\ \left(\sin\ \alpha\right)\left(\sin\ \beta\right)$

31.

$\cos\ \left(\alpha\ +\ \beta\right)$

a)

$\left(\sin\ \alpha\right)\left(\cos\ \beta\right)\ -\ \left(\cos\ \alpha\right)\left(\sin\ \beta\right)$

b)

$\left(\sin\ \alpha\right)\left(\cos\ \beta\right)\ +\ \left(\cos\ \alpha\right)\left(\sin\ \beta\right)$

c)

$\left(\cos\ \alpha\right)\left(\cos\ \beta\right)\ -\ \left(\sin\ \alpha\right)\left(\sin\ \beta\right)$

d)

$\left(\cos\ \alpha\right)\left(\cos\ \beta\right)\ +\ \left(\sin\ \alpha\right)\left(\sin\ \beta\right)$

32.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

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

c)

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

d)

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

33.

$\tan\left(20\right)=$

a)

$\frac{\tan30+\tan10}{1+\tan30\tan10}$

b)

$\frac{\tan30-\tan10}{1-\tan30\tan10}$

c)

$\frac{\tan30-\tan10}{1+\tan30\tan10}$

d)

$\frac{\tan30+\tan10}{1-\tan30\tan10}$

34.

Find the exact value of the expression.
sin(5π/12)cos(π/4) - cos(5π/12)sin(π/4)

a)

1/2

b)

-1/2

c)

-√(2)/2

d)

√(3)/2

35.

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

36.

Convert from polar coordinates, (20, 11π/6) to rectangular coordinates.

a)

(-10√3, 10)

b)

(10√3, -10)

c)

(10, -10√3)

d)

(10√2, -10)

37.

Convert from rectangular to polar coordinates. (-4, 4)

a)

(4√2, π/4)

b)

(4√2, 3π/4)

c)

(4√2, -π/4)

d)

(-4√2, -7π/4)

38.

What complex number is shown on the graph?

a)

(-2,-3)

b)

$-2-3i$

c)

$2-3i$

d)

$-3-2i$

39.

Write the complex number in polar form

a)

√50 (cos π/2 + i sin π/2)

b)

50 (cos π/4 + i sin π/4)

c)

√50 (cos 5π/4 + i sin 5π/4)

d)

√50 (cos π/4 + i sin π/4)

40.

Write the complex number in polar form

a)

3 ( cos 3π/2 + i sin 3π/2)

b)

3 ( cos π/2 + i sin π/2)

c)

9 ( cos 3π/2 + i sin 3π/2)

d)

3 ( cos 2π + i 2π)

41.

Express the point in polar form in rectangular form.
4(cos π/3 + i sin π/3)

Remember, this can be written 4 cis π/3

a)

2 + 2√3 i

b)

2 + √3 i

c)

2 - 2√3 i

d)

-2 + 2√3 i

42.

If z = 2(cos(20) + isin(20)) and w = 3(cos(105) + isin(105)), find z / w. Choose all that apply.

a)

2/3(cos(-85) + isin(-85))

b)

2/3(cos(275) + isin(275))

c)

3/2(cos(85) + isin(85))

d)

6(cos(125) + isin(125))

43.

Find the indicated power using DeMoivre's Theorem

a)

72 - 72√3i

b)

- 72√3 + 72i

c)

- 72√2 + 72√2i

d)

-72 + 72√3i

44.

Which of the following could be the equation for...

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

45.

Which of these is an equation for this dimpled limaçon?

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 2 - 3cosθ

46.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

47.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

48.

This particular equation generates what graph

a)

b)

c)

d)

49.

What is the polar equation of the graph shown here?

a)

$\theta=-\frac{\pi}{4}$

b)

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

c)

$\theta=\pi$

d)

$\theta=\frac{\pi}{6}$

50.

Identify the equation in the polar graph

a)

$r\ =7+4\sin\theta$

b)

$r\ =\ 7+4\cos\theta$

c)

$r\ =\ 4+7\sin\theta$

d)

$r\ =4+7\cos\theta$

51.

Which of these is the equation of the graph shown?

a)

$r=5\cos4\theta$

b)

$r=5\sin5\theta$

c)

$r=4\cos8\theta$

d)

$r=5\cos8\theta$

e)

$r=5\sin4\theta$

52.

Which of the following could be the equation for...

a)

r = 2cos(7θ)

b)

r = 7sin(14θ)

c)

r = 2sin(7θ)

d)

r = 2sin(14θ)

e)

r = 2sin(3.5θ)

53.

Which interval creates the loop (highlighted) of

r = 2 + 4 cosθ

a)

$\left[0,\frac{\pi}{3}\right]$

b)

$\left[\frac{\pi}{3},\ \frac{2\pi}{3}\right]$

c)

$\left[\frac{2\pi}{3},\ \frac{4\pi}{3}\right]$

d)

$\left[\frac{4\pi}{3},\ \frac{5\pi}{3}\right]$

e)

$\left[\frac{5\pi}{3},\ 2\pi\right)$

54.

Identify the interval of the red portion of this graph.

a)

$\left[\frac{\pi}{3},\ \frac{\pi}{2}\right]$

b)

$\left[\frac{\pi}{2},\ \frac{2\pi}{3}\right]$

c)

$\left[\frac{2\pi}{3},\ \frac{5\pi}{6}\right]$

d)

$\left[\frac{5\pi}{6},\ \pi\right]$

55.

Find the average rate of change on the interval $\left[\frac{2\pi}{3},\ \frac{5\pi}{6}\right]$

a)

$\frac{36}{\pi}units\ per\ radian$

b)

$\frac{\pi}{36}radians\ per\ unit$

c)

$-\frac{36}{\pi}units\ per\ radian$

d)

$-\frac{\pi}{36}radians\ per\ unit$

BC PreCalc Final Review Sem. 2

Total questions: 55

Worksheet time: 40mins

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