Free Printable 5 PRECALCULUS

1.

The __________ is a set of all points in which the sum of the distances between a point to two fixed point is constant.

a)

CIRCLE

b)

PARABOLA

c)

ELLIPSE

d)

HYPERBOLA

2.

What do you call the two fixed points of an ellipse?

a)

Focus

b)

Foci

c)

Directrix

d)

vertex

3.

Find the center and vertices of the ellipse: $\frac{x^2}{49}+\frac{y^2}{4}=1$

a)

Center: (7,0) vertices: (0,-2)(0,2)

b)

Center: (0,0) vertices: (-2,0)(2,0)

c)

Center: (0,0) vertices: (0,-7)(0,7)

d)

Center: (0,0) vertices: (-7,0)(7,0)

4.

Find the equation of the ellipse that has its center at the origin with focus at (0,4) and vertex at (0,7).

a)

$\frac{x^2}{49}+\frac{y^2}{33}=1$

b)

$\frac{x^2}{49}-\frac{y^2}{33}=1$

c)

$\frac{x^2}{33}-\frac{y^2}{49}=1$

d)

$\frac{x^2}{33}+\frac{y^2}{49}=1$

5.

Which of the following is the graph of the equation of the ellipse: $\frac{\left(x-1\right)^2}{9}+\frac{\left(y+5\right)^2}{4}=1$

a)

b)

c)

d)

6.

Given $x^2-2y^2-4x+12y-18=0$ , what is the center of this hyperbola?

a)

$(-2,-3)$

b)

$(2,3)$

c)

( 3,2 )

d)

(2, -3)

7.

Given $x^2-2y^2-4x+12y-18=0$ , which of the following is a vertex of the given hyperbola?

a)

(0,3)

b)

(3,0)

c)

(-2,3)

d)

(3,-2)

8.

Given the hyperbola $9x^2-25y^2=225$ , find the length of the conjugate axis.

a)

5 units

b)

3 units

c)

10 units

d)

6 units

9.

Given the hyperbola $9x^2-25y^2=225$ , find the coordinates of the foci

a)

$(0,\pm\sqrt{34})$

b)

$(\pm\sqrt{34},0)$

c)

$\left(\pm5,0\right)$

d)

$\left(0,\pm5\right)$

10.

The __________ is a set of all point in which the difference between the any point to the two fixed point is constant.

a)

CIRCLE

b)

ELLIPSE

c)

HYPERBOLA

d)

PARABOLA

11.

It is the line in which the hyperbola approaches but never touches.

a)

ASYMPTOTES

b)

CENTRAL BOX

c)

CONJUGATE AXIS

d)

TRANSVERSE AXIS

12.

It is a closed figure drawn using the value of a, and b, which guides in drawing the asymptotes and the hyperbola

a)

CENTRAL TRIANGLE

b)

CENTRAL CENTER

c)

CENTRAL BOX

d)

ASYMPTOTES

13.

Write the standard form equation of the hyperbola given the following:

Center at (-6, 9), Vertex at (-18, 9), Eccentricity = $\frac{5}{4}$

4 lines

14.

In an angle, the common end point is known as

a)

vertex

b)

point of intersection

c)

initial side

d)

terminal side

15.

A full revolution of a circle is equivalent to

a)

180\degree

b)

$2\pi\ radian$

c)

$360\ mm$

d)

$90\ rev$

16.

It refers to the length of a line that bounds a circle.

a)

arc

b)

radian

c)

circumference

d)

radius

17.

$270\degree$ is equivalent to?

a)

$\pi$

b)

$2\pi$

c)

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

d)

$\frac{\pi}{4}$

18.

$\frac{\pi}{9}$

Convert the angle measure into degrees

a)

$20\degree$

b)

$30\degree$

c)

$35\degree$

d)

$60\degree$

19.

What is the measure of a given angle in radians if its arc length is 4π and the radius has a length of 12 ?

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}$

c)

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

d)

$3\pi$

20.

It is the measure of an angle formed when the initial side rotates all the way around its vertex until it reaches its initial position.

a)

arc length

b)

revolution

c)

circumference

d)

area

21.

Which of the following is not an example of coterminal angles?

a)

$45\degree\ and\ -315\degree$

b)

$30\degree,\ 390\degree,\ and\ -330\degree$

c)

$\frac{\pi}{3}\ and\ -5\frac{\pi}{3}$

d)

$\frac{\pi}{6}\ and\ \frac{7\pi}{6}$

22.

What is the reference angle of the 135 degrees?

a)

$10\degree$

b)

$15\degree$

c)

$35\degree$

d)

$45\degree$

23.

Which of the following is an example of a quadrantal angle?

a)

$45\degree$

b)

$60\degree$

c)

$135\degree$

d)

$360\degree$

24.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

25.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

(3, -5) and (3, 7)

d)

(3, 1)

26.

In an ellipse, what distance does a represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

27.

In an ellipse, what distance does b represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

28.

In an ellipse, what distance does c represent?

a)

The distance from the center to a vertex

b)

The distance from the center to a co-vertex

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

29.

In an ellipse, what is the length of the minor axis?

a)

a

b)

2a

c)

b

d)

2b

e)

c

30.

The major axis is...

a)

the x-axis

b)

the y-axis

31.

The line containing the center and foci.

a)

Major Axis

b)

Minor Axis

c)

Vertices

d)

Co-Vertices

32.

Write the standard form of the ellipse:

9x² + 4y² +72x +108=0

a)

(x-4)² /16 + y ²/ 36 = 1

b)

(x+4)² /4 + y ²/ 9 = 1

c)

(x-4)² /4 + y ²/ 9 = 1

d)

(x+4)² /16 + y ²/ 36 = 1

33.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

34.

Foci?

a)

(-3 , 4) and (-3 , 0)

b)

(3 , -4) and (3 , 0)

c)

(-3 , -4) and (-3 , 0)

d)

(-3 , 4) and (3 , 0)

35.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

36.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

37.

Simplify (Hint: you will need to FOIL first)

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

38.

Simplify

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

39.

Simplify: tanxcotx-cos²x

a)

tanx

b)

cotx

c)

sin²x

d)

cos²x

40.

Verify the following.
tanB (cotB + tanB) = sec²B

a)

1+ tan²B

b)

sec²B

c)

cot²B

d)

tan²B

41.

Verify the following:

a)

cos²x

b)

sin²x

c)

cot²x

d)

tan²x

42.

Solve $2\sin x+1=0$ on the interval $\left[o,\ 2\pi\right]$

a)

$\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\frac{\pi}{6},\frac{5\pi}{6}$

c)

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

d)

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

43.

Find the exact value of $\sin285\degree$

a)

$\frac{\left(\sqrt{6}+\sqrt{2}\right)}{4}$

b)

$\frac{\left(-\sqrt{6}-\sqrt{2}\right)}{4}$

c)

$\frac{\left(\sqrt{6}+\sqrt{2}\right)}{2}$

d)

$\frac{\left(-\sqrt{6}-\sqrt{2}\right)}{2}$

44.

$\frac{1}{\sin\theta-1}-\frac{1}{\sin\theta+1}$ Simplify

a)

$2\csc^2\theta$

b)

$-2\csc^2\theta$

c)

$2\sec^2\theta$

d)

$-2\sec^{2\ }\theta$

45.

Find an expression equivalent to
$\frac{\sec^2\theta}{\tan\theta+\cot^2\theta\tan\theta}$ containing only one trig function.

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\tan\theta$

d)

$\cot\theta$

46.

Solve

$2\cos x-\sin^{2\ }x+2=0$

for all values of x

a)

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

b)

$\frac{\pi}{2}$

c)

$\pi+2\pi n$

d)

$\pi$

47.

Find the exact value of

$-\sin75\degree$

a)

$-\frac{\left(\sqrt{6}+\sqrt{2}\right)}{4}$

b)

$\frac{\left(\sqrt{6}+\sqrt{2}\right)}{4}$

c)

$\frac{\left(-\sqrt{6}+\sqrt{2}\right)}{4}$

d)

$\frac{\left(\sqrt{6}-\sqrt{2}\right)}{4}$

48.

^{What is the x- intercept of the line?}

a)

(0,-1)

b)

(-2,0)

c)

(-1,0)

d)

(0,-2)

49.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

50.

What is the y-intercept?

a)

(0,7)

b)

(0,0)

c)

(1,9)

d)

(2,11)

51.

a)

$y=x^2+9$

b)

$y=-x^2+9$

c)

$y=x^2-9$

d)

$y=-x^2-9$

52.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

53.

What quadratic does this area diagram represent?

a)

$x^2+7x+12$

b)

$x^2+8x+12$

c)

$x^2+7x+10$

d)

$x^2+8x+10$

54.

Simplify: $\left(a+b\right)^2$

a)

$a^2+b^2$

b)

$a^2+2ab+b^2$

c)

$\sqrt{a+b}$

d)

$ab^4$

55.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

56.

Simplify the expression.

$\frac{b^7\times b^3}{b^2}$

a)

$b^5$

b)

$b^8$

c)

$b^{19}$

d)

$b^{10}$

57.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

58.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

59.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

60.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

61.

Find the volume of the Sphere

a)

78.5 m³

b)

392.5 m³

c)

523.6 m³

d)

62.8 cm³

62.

∣ 2x + 9 ∣ = 15

a)

x = 3

b)

x = 3
x = -6

c)

x = 3
x = -12

d)

x = 6
x = -12

63.

What type of sequence is this?

5, 9/2, 4, 7/2, 3, 5/2, 2

a)

Arithmetic sequence

b)

Arithmetic series

c)

Harmonic sequence

d)

Geometric sequence

64.

The sum of the first n terms of an arithmetic series is -85.5. The first term of the series is -27/3 and the common difference is 1/2. How many terms are in the series?

a)

16

b)

17

c)

18

d)

20

65.

What is the sum of the first 35 terms in an arithmetic series with the first term 18, common difference -12?

a)

770

b)

775

c)

870

d)

875

66.

Find the sum of the first 105 terms in an arithmetic series with the first term 95876 is 7, 271, 880. Find the last term?

a)

6998

b)

6754

c)

7168

d)

72636

67.

Find the sum of the first 15 terms in a geometric series with the first term 81, 920 and the ratio 1/2.

a)

32/3

b)

5

c)

18

d)

1589/3

68.

Find the sum of the first 20 terms in a geometric series with the first term 9 and the common ratio -1.

a)

-20

b)

20

c)

15

d)

415/2

69.

Find the sum of the the following series

2+6+18+54+....

a)

-1

b)

1

c)

infinity

d)

No sum

70.

Find the sum of the following sequence

9, 13.5, 20.25, 30.375, ...

a)

-18

b)

18

c)

No sum

71.

Find the sum of the following series

2+4/3+8/9+16/27+ ...

a)

So sum

b)

6

c)

-6

72.

Expand the summation.

a)

-1800

b)

-1818

c)

-1825

d)

-1795

73.

Expand and simplify

a)

802

b)

1002

c)

1396

d)

1755

74.

Expand and simplify if possible.

a)

b)

c)

d)

75.

Write the expression in sigma notation

a)

b)

c)

d)

76.

Expand the expression

a)

b)

c)

d)

77.

Expand the expression

a)

b)

c)

d)

78.

a)

b)

c)

d)

79.

How many terms are there in the expansion

a)

100

b)

97

c)

99

d)

101

80.

a)

b)

c)

d)

81.

What is the formula to find the nth term of an arithmetic series?

a)

a_n = a_1 * (n-1)d

b)

a_n = a_1 + (n-1)d

c)

a_n = a_1 - (n-1)d

d)

a_n = a_1 / (n-1)d

82.

Find the sum of the arithmetic series: 2 + 5 + 8 + 11 + ... + 23, if there are 8 terms.

a)

132

b)

100

c)

78

d)

56

83.

Write the summation notation for the arithmetic series: 3 + 6 + 9 + ... + 27.

a)

∑(3n+3) from n=1 to 9

b)

∑(3n) from n=1 to 9

c)

∑(3 + 3n) from n=1 to 9

d)

∑(3n-3) from n=1 to 9

84.

What is the formula to find the sum of an arithmetic series?

a)

n(a - l)

b)

n(a + l)

c)

(n/2)(a - l)

d)

(n/2)(a + l)

85.

Find the sum of the arithmetic series: 10 + 15 + 20 + ... + 50, if there are 9 terms.

a)

275

b)

400

c)

240

d)

325

86.

Write the summation notation for the arithmetic series: 4 + 8 + 12 + ... + 40.

a)

∑(4 + 4n) from n=0 to 9

b)

∑(4 + 2n) from n=0 to 10

c)

∑(4 + 5n) from n=0 to 8

d)

∑(4 + 3n) from n=0 to 9

87.

What is the formula to find the nth term of a geometric series?

a)

a * r^(n-1)

b)

a * r^n

c)

a + r^(n-1)

d)

a * (r-1)^(n-1)

88.

Find the sum of the geometric series: 2 + 4 + 8 + 16 + ... + 256, if there are 6 terms.

a)

340

b)

768

c)

510

d)

1020

89.

Write the summation notation for the geometric series: 5 + 10 + 20 + ... + 320.

a)

∑(5 * 2^(n+1)) from n=1 to 7

b)

∑(5 * n) from n=1 to 7

c)

∑(5 * 2^(n-1)) from n=1 to 7

d)

∑(5 + 2^(n-1)) from n=1 to 7

90.

What is the formula to find the sum of a geometric series?

a)

S = a + r

b)

S = a / (1 - r)

c)

S = a * r

d)

S = a - r

91.

Find the first 6 terms of the sequence.

a)

13, 19, 25, 31, 37, 43

b)

7, 13, 19, 25, 31, 37

c)

1, 7, 13, 19, 25, 31

d)

7, 12, 17, 22, 27, 32

92.

Find the first 6 terms of the sequence

a)

1, 2, 6, 18, 54, 162

b)

2, 6, 18, 54, 162, 486

c)

-2, -6, -18, -54, -162, -486

d)

-2, 1, 4, 7, 10, 13

93.

Find an explicit rule for the nth term of the sequence.

a)

a_n= 15+(n-1)4

b)

a_n= -15+(n-1)4

c)

a_n= -15+(n-1)3

d)

a_n= 4n -19

94.

Find the sum of the arithmetic series using a formula.

a)

516, 240

b)

516,242

c)

116, 242

d)

506, 242

95.

Find the sum of the geometric series.

a)

732

b)

-732

c)

244

d)

-244

96.

Find the explicit rule for the nth term of the sequence. The second and fifth terms of a geometric sequence are -24 and 1536, respectively.

a)

a_n= 6(-4)^n-1

b)

a_n= 6×-4^n-1

c)

a_n= 6(-4)ⁿ

d)

a_n= -6(4)^n-1

97.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

98.

When using mathematical induction to prove : $\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ . In step #2, after you have made your assumption, what are you trying to prove? (What is your goal?)

a)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$

b)

$S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$

c)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$

d)

$S_{k+1}=\left(k+1\right)^2$

99.

Let S(n) = 2n − 1. Evaluate:
a) S(k)
b) S(k + 1)

a)

a) S(k) = 2k − 1
b) S(k + 1) = 2n + 1

b)

a) S(k) = 2k + 1
b) S(k + 1) = 2k + 1

c)

a) S(k) = 2k − 1
b) S(k + 1) = 2k + 1

100.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²
On the basis of this assumption,
[The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]
What must we show?

a)

The statement is true for n = 1:
2x1 − 1 = 1²

b)

The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

101.

The sum of the first n odd numbers is equal to the n^th square.
1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

To prove this by mathematical induction, what will be the induction assumption?

a)

The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

b)

The statement is true for n = 1:
2x1 − 1 = 1²

c)

The statement is true for n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

102.

In the principle of mathematical induction, what is the term for the first condition?

a)

Base case

b)

First case

c)

Inductive case

d)

Introductory case

103.

What is the mathematical term for the second condition of the principle of mathematical induction?

a)

Base case

b)

First case

c)

Inductive case

d)

Introductory case

104.

What is the third step in Mathematical induction?

a)

P(1)

b)

P(k+1)

c)

P(k)

d)

n=k

105.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

On the basis of this assumption, [The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]

What must we show next?

a)

The statement is true for n = 1:

(2)(1) − 1 = 1²

b)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

106.

Let P(n) = 2n − 1. Evaluate:

a) P(k)

b) P(k + 1)

a)

a) P(k) = 2k − 1

b) P(k + 1) = 2n + 1

b)

a) P(k) = 2k + 1

b) P(k + 1) = 2(k + 1) - 1

c)

a) P(k) = 2k − 1

b) P(k + 1) = 2k + 1

107.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

To prove this by mathematical induction, what will be the induction assumption?

a)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

b)

The statement is true for n = 1:

(2)(1) − 1 = 1²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

108.

What is the first step in Mathematical Induction?

a)

P(k)

b)

n=k

c)

P(k+1)

d)

P(1)

109.

What do you call the statement to be prove?

a)

Inductive statement

b)

Structure

c)

Conjecture

d)

Given

110.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the first?

a)

The statement is true for n = 1.

b)

The statement is true for n = k.

c)

The statement is true for n = k+1.

111.

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the second?

a)

The statement is true for n = k+1.

b)

If the statement is true for n = k, then it will be true for its successor, k + 1.

c)

The statement is true for n = 1.

d)

The statement is true for n = k.

112.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²
On the basis of this assumption,
[The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]
What must we show?

a)

The statement is true for n = 1:
2x1 − 1 = 1²

b)

The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

113.

Where does the number 5 belong?

a)

2,4,6,8,10,...

b)

100,90,80,70,60,...

c)

3,6,9,12,15,.....

d)

50,45,40,35,...

114.

Let S(n) = 2n − 1. Evaluate:
a) S(k)
b) S(k + 1)

a)

a) S(k) = 2k − 1
b) S(k + 1) = 2n + 1

b)

a) S(k) = 2k + 1
b) S(k + 1) = 2k + 1

c)

a) S(k) = 2k − 1
b) S(k + 1) = 2k + 1

115.

The sum of the first n odd numbers is equal to the n^th square.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

Which of the following illustrates S_k?

a)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

b)

The statement is true for n = 1:

2x1 − 1 = 1²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

116.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

On the basis of this assumption,

[The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]

What must we show next?

a)

The statement is true for n = 1:

2x1 − 1 = 1²

b)

The statement is true for n = k:

1 + 3 + 5 + 7 + . . . + (2k − 1) = k²

c)

The statement is true for n = k + 1:

1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

117.

$\sum_{i=1}^ni^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ Given that the statement above is true for n=k, which of the following should be proven true?

a)

$\sum_{i=1}^{k+1}i^2=\frac{\left(k\right)\left(k+1\right)\left(2k+1\right)}{6}+\left(k+1\right)^2$

b)

$S_{k+1}=\frac{k\left(k+1\right)\left(2k+1\right)}{6}$

c)

$\sum_{k=1}^n\left(k+1\right)^2=\frac{\left(k+1\right)\left(k+2\right)\left(2k+3\right)}{6}$

d)

$S_{k+1}=\left(k+1\right)^2$

118.

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places.

sec 1.8

(a)

119.

Evaluate the trigonometric function using its period as an aid.

sin $\frac{19\pi}{4}$

a)

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

b)

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

c)

$\frac{1}{2}$

d)

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

120.

Convert the angle measure from degrees to radians. Round to three decimal places if you choose to write in that form.

$532\degree$

a)

$9.284\ =\ \frac{12\pi}{5}$

b)

$9.280\ =\ \frac{133\pi}{45}$

c)

$9.325\ =\ \frac{15\pi}{6}$

d)

$9.477\ =\frac{17\pi}{2}$

121.

Convert the angle measure from radians to degrees. Round to three decimal places.

\frac{15\pi}{8}

a)

$333.500$

b)

$337.500\degree$

c)

$323.513\degree$

d)

$\pi$

122.

Determine two coterminal angles (one positive and one negative) for each angle. Give your answer in radians.

$-\frac{11\pi}{6}$

a)

$\frac{\pi}{7}\ and\ -\frac{13\pi}{6}$

b)

$\frac{3\pi}{2}\ and\ -\ \frac{17\pi}{2}$

c)

$\frac{\pi}{6}\ and\ \ -\frac{23\pi}{6}$

d)

$-\frac{\pi}{6}\ and\ \frac{13\pi}{6}$

123.

$\frac{5\pi}{3}$ Find the point (x,y) on the unit circle that corresponds to the real number t.

a)

$\left(-\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

b)

$\left(\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)$

c)

$\left(\frac{1}{2},\ -\frac{\sqrt{3}}{2}\right)$

d)

$\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

124.

Evaluate (if possible) the sine and cotangent functions of the real number.
$\frac{4\pi}{3}$

a)

$\sin\ t\ =\ \frac{\sqrt{3}}{2}\ and\ \cot\ t=\sqrt{3}$

b)

$\sin t\ =\ \frac{1}{2}\ and\ \cot\ t=\frac{\sqrt{3}}{2}$

c)

$\sin t\ =\ \frac{\sqrt{2}}{2}\ and\ \cot\ t=\frac{1}{2}$

d)

$\sin\ t\ =\ -\frac{\sqrt{3}}{2}\ and\ \cot\ t\ =\ \frac{\sqrt{3}}{3}$

125.

Use the given value(s), and the trigonometric identities, to find the indicated trigonometric functions.
Given:
$\sec\ \theta=5\ and\ \tan\ \theta\ =2\sqrt{6}$

FIND:

\cos\ \theta,\ \cot\ \theta,\ and\ \sin\ \theta

a)

$\cos\ \theta\ =\ \frac{1}{5},\ \cot\ \theta=\sqrt{3},\ and\ \sin\ \theta=\frac{\sqrt{3}}{2}$

b)

$\cos\ \theta=5,\ \cot\ \theta=\frac{1}{5},\ and\ \sin\ \theta=\ \frac{\sqrt{6}}{12}$

c)

$\cos\ \theta=\frac{1}{5},\ \cot\ \theta=\frac{\sqrt{6}}{12},\ and\ \sin\ \theta=\frac{2\sqrt{6}}{5}$

d)

$\cos\ \theta=\frac{1}{2},\ \cot\ \theta=\frac{\sqrt{5}}{3},\ and\ \sin\ \theta=\ 3$

126.

Use a calculator to evaluate the function. Round your answer to four decimal places.
$\cot\ 66.5\degree$

(a)

127.

Find the values of the angle in degrees and radians without the aid of a calculator. (HINT: use Quadrant I)

\cot\ \theta=\frac{\sqrt{3}}{3}

a)

$\theta=\ 45\degree\ or\ \frac{\pi}{4}$

b)

$\theta=30\degree\ or\ \frac{\pi}{6}$

c)

$\theta=90\degree\ or\ \frac{\pi}{2}$

d)

$\theta\ =60\degree\ or\ \frac{\pi}{3}$

128.

Evaluate the trigonometric function using its period as an aid.

sin $\frac{19\pi}{4}$

a)

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

b)

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

c)

$\frac{1}{2}$

d)

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

129.

Convert the angle measure from degrees to radians. Round to three decimal places if you choose to write in that form.

$532\degree$

a)

$9.284\ =\ \frac{12\pi}{5}$

b)

$9.280\ =\ \frac{133\pi}{45}$

c)

$9.325\ =\ \frac{15\pi}{6}$

d)

$9.477\ =\frac{17\pi}{2}$

130.

Convert the angle measure from radians to degrees. Round to three decimal places.

\frac{15\pi}{8}

a)

$333.500$

b)

$337.500\degree$

c)

$323.513\degree$

d)

$\pi$

131.

$\frac{5\pi}{3}$ Find the point (x,y) on the unit circle that corresponds to the real number t.

a)

$\left(-\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

b)

$\left(\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)$

c)

$\left(\frac{1}{2},\ -\frac{\sqrt{3}}{2}\right)$

d)

$\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

132.

Use the given value(s), and the trigonometric identities, to find the indicated trigonometric functions.
Given:
$\sec\ \theta=5\ and\ \tan\ \theta\ =2\sqrt{6}$

FIND:

\cos\ \theta,\ \cot\ \theta,\ and\ \sin\ \theta

a)

$\cos\ \theta\ =\ \frac{1}{5},\ \cot\ \theta=\sqrt{3},\ and\ \sin\ \theta=\frac{\sqrt{3}}{2}$

b)

$\cos\ \theta=5,\ \cot\ \theta=\frac{1}{5},\ and\ \sin\ \theta=\ \frac{\sqrt{6}}{12}$

c)

$\cos\ \theta=\frac{1}{5},\ \cot\ \theta=\frac{\sqrt{6}}{12},\ and\ \sin\ \theta=\frac{2\sqrt{6}}{5}$

d)

$\cos\ \theta=\frac{1}{2},\ \cot\ \theta=\frac{\sqrt{5}}{3},\ and\ \sin\ \theta=\ 3$

133.

Find the values of the angle in degrees and radians without the aid of a calculator. (HINT: use Quadrant I)

\cot\ \theta=\frac{\sqrt{3}}{3}

a)

$\theta=\ 45\degree\ or\ \frac{\pi}{4}$

b)

$\theta=30\degree\ or\ \frac{\pi}{6}$

c)

$\theta=90\degree\ or\ \frac{\pi}{2}$

d)

$\theta\ =60\degree\ or\ \frac{\pi}{3}$

134.

Find the length of BC.

a)

17.0

b)

21.9

c)

18.6

d)

22.4

135.

sin x = _____

a)

1/csc x

b)

1/sec x

c)

1/cos x

d)

1/cot x

136.

A cosine equation has an amplitude of 4, a period of $\pi$ , and its midline is y = -1.

Find the equation of this function.

a)

f(x) = -4cos(2x) - 1

b)

f(x) = 4cos( $\pi$ x) -1

c)

f(x)= cos( $\pi$ x) + 4

d)

f(x)= -cos(undefinedx) + 4

137.

Which of the following is equivalent to tanx?

a)

$\frac{1}{\frac{\cos x}{\sin x}}$

b)

$\frac{\cos x}{\sin x}$

c)

$\sec\ x-1$

d)

$1-\sec\ x$

138.

What is the period of either graph?
y = sin(x) & y = cos (x)

a)

Pi

b)

2Pi

c)

Pi/2

d)

Pi/4

139.

what is the amplitude of
y = 3sin (7x) -2

a)

7

b)

-2

c)

3

d)

6

140.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

141.

What is the maximum value of the wave y = 10sin(2x - 20) + 25?

a)

10

b)

20

c)

35

d)

30

142.

A trig function has an amplitude of 4 and a minimum value of 5. What is its maximum value?

a)

7

b)

9

c)

11

d)

13

143.

$\frac{1-\cos^2\theta}{\cos^2\theta}$ can be written in a single trigonometric identity as:

a)

$\cos^2\theta$

b)

$\sin^2\theta$

c)

$\sec^2\theta$

d)

$\tan^2\theta$

144.

Simplify

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

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

145.

Simplify

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

a)

$\sec\theta$

b)

$\cos^2\theta$

c)

$\sin^2\theta$

d)

$\frac{\sin^2\theta}{\cos^2\theta}$

146.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

147.

Simplify

$\tan x\csc x\cos x$

a)

$\frac{1}{\cos x}$

b)

1

c)

$\cot x$

d)

-1

148.

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

a)

$2\sec\theta$

b)

$\cot^2\theta$

c)

$\tan^2\theta$

d)

$\sec^2\theta+1$

149.

Simplify

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

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

150.

a)

csc x

b)

sec x

c)

1/sec x

d)

cos x

151.

Simplify: $\frac{\sec^2x}{\sec^2x-1}$

a)

$\sin^2x$

b)

$\csc^2x$

c)

$\cos^2x$

d)

$\sec^2x$

152.

Which of the following is equivalent to $\sin\left(\alpha+\beta\right)$ ?

a)

$\sin\alpha\cos\alpha+\sin\beta\cos\beta$

b)

$\sin\alpha\cos\alpha-\sin\beta\cos\beta$

c)

$\sin\alpha\cos\beta+\cos\alpha\sin\beta$

d)

$\sin\alpha\cos\beta-\cos\alpha\sin\beta$

153.

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)

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

154.

Which of the following is a solution of the equation

√3 sec θ = 2

a)

-π/3

b)

π/6

c)

π/4

d)

π

155.

Which of the following is false?

a)

$\sin\left(-x\right)=-\sin\left(x\right)$

b)

$\cos\left(-x\right)=-\cos\left(x\right)$

c)

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

d)

$\cot\left(-x\right)=-\cot\left(x\right)$

5 PRECALCULUS

Total questions: 155

Worksheet time: 5hrs 10mins

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