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Berkeley City College
Homework Due:_______________________
Precalculus - Math 1 - Chapter 6 Introduction to Trigonometry
Name___________________________________
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
1) 50°
1)
A) 410° and -310°
B) 410° and -310°
C) 230° and -130°
D) 230° and -130°
Evaluate the expression.
2) sec(-90°)
A) Undefined
2)
B)
2 3
3
D) -1
C) 0
3) cot 450°
A) 0
3)
B) 1
C)
2
2
D) Undefined
4) sin(-180°)
A) 0
4)
B) Undefined
C) 1
D) -1
5) 5 tan 180° + 9 csc 270°
A) Undefined
Instructor: K. Pernell
5)
B) -9
C) 9
1
D) 0
6) cos 360° - 5 sin 90°
A) -4
6)
B) -5
C) 1
D) 0
Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the
indicated trig function for θ.
7)
7) (4, 5); Find tan θ.
A)
4
5
B)
5
6
C)
2
3
D)
5
4
8) (-20, 48); Find sin θ.
A) - 5
13
8)
B)
5
13
C)
12
13
D) - 9) (12, 16); Find sin θ.
A)
4
3
12
13
9)
B)
3
5
C)
2
4
5
D)
3
4
Sketch an angle θ in standard position such that θ has the smallest positive measure and the given point is on the
terminal side of θ.
10)
10) (-2, 5)
y
x
A)
B)
C)
D)
Identify the quadrant for the angle θ satisfying the following conditions.
11) cot θ < 0 and cos θ > 0
A) Quadrant I
B) Quadrant III
C) Quadrant IV
11)
D) Quadrant II
12) sin θ > 0 and cos θ < 0
A) Quadrant IV
12)
B) Quadrant III
C) Quadrant II
3
D) Quadrant I
13) tan θ > 0 and sin θ < 0
A) Quadrant IV
13)
B) Quadrant II
C) Quadrant III
D) Quadrant I
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
14) csc (558°) and cot (558°)
14)
A) positive and positive
B) positive and negative
C) negative and positive
D) negative and negative
15) cos (433°) and sin (433°)
15)
A) negative and positive
B) negative and negative
C) positive and positive
D) positive and negative
Use the fundamental identities to find the value of the trigonometric function.
3
16) Find sec θ, given that tan θ = and θ is in quadrant I.
4
A)
3 7
7
B) - 7
9
C)
5
4
16)
D) - 3
2
2
17) Find sin θ, given that cos θ = and θ is in quadrant IV.
3
A)
3 7
7
B) - 18) Find csc θ, given that cot θ = - A) - 3 109
109
B)
5
3
C)
17)
5
4
D) - 3
2
3
and cos θ < 0.
10
18)
3 109
109
C) - 109
3
D)
109
10
2
19) Find sin θ, given that cos θ = and tan θ < 0.
9
A) - 9
2
19)
B) - 77
C) - 4
77
2
D) - 77
9
Solve the problem.
20) Find the exact value of x in the figure.
20)
14
x
A) 7 6
B) 7 3
C)
14 3
3
D)
14 6
3
21) Find the exact value of x in the figure.
21)
34
A) 17 3
B) 17 6
C) 15 3
D) 18 3
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
22)
22) Find tan B when a = 96 and c = 100.
A)
24
25
B)
24
7
C)
7
25
D)
7
24
23) Find sin A when b = 24 and c = 40
A)
3
4
B)
23)
3
5
C)
5
4
5
D)
5
4
Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
3
24) sin θ = 2
A) 60° and 120°
25) cos θ = B) 60° and 300°
C) 150° and 210°
24)
D) 210° and 330°
1
2
A) 150° and 210°
25)
B) 60° and 300°
C) 210° and 330°
D) 60° and 120°
Give the exact value.
26) csc 330°
A) -2
26)
B)
2 3
3
D) - C) 2
2 3
3
27) sec 150°
A) 27)
2 3
3
B) - 2
C) - 2 3
3
D)
2
28) cot 120°
28)
A) - 3
B) - 3
3
C) -1
D)
3
3
29) tan 300°
A) 29)
3
3
B) - 3
3
C) - 3
D)
3
30) cos 210°
A) - 30)
2
2
B) 3
2
C) - 6
3
2
D) 2
2
Find the exact trigonometric function value.
31) cos 960°
A) - 3
2
31)
B) - 3
C) - 1
2
D)
2
2
32) sin (-1680°)
A)
3
2
32)
B) -1
C)
2
2
D)
1
2
Find the reference angle for the given angle.
33) -400°
A) 130°
33)
B) 50°
C) 140°
D) 40°
34) 211.4°
A) 31.4°
34)
B) 121.4°
C) 148.6°
D) 58.6°
35) 138°
A) 42°
35)
B) 58°
C) 52°
D) 48°
36) 78°
A) 12°
36)
B) 102°
C) 168°
D) 78°
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
csc x cot x
37)
37)
sec x
A) 1
B) cot2 x
C) csc2 x
D) sec 2 x
38) csc x(sin x + cos x)
A) -2 tan2 x
38)
B) sin x tan x
C) sec x csc x
7
D) 1 + cot x
Factor the trigonometric expression and simplify.
39) sin2 x + sin2 x cot2 x
A) 1
39)
B) cot2 x + 1
C) sin2 x + 1
D) cot2 x - 1
40) 1 - 2 sin2 x + sin4 x
A) (1 - sin2 x)
40)
B) sin2 x
C) cos4 x
D) (1 + tan 2 x)
Perform the indicated operations and simplify the result.
sin θ cos θ
41)
+ cos θ sin θ
A) sin θ tan θ
42)
41)
B) 1 + cot θ
C) sec θ csc θ
D) -2 tan2 θ
sin θ
sin θ
- 1 + sin θ 1 - sin θ
A) 1 + cot θ
42)
B) -2 tan2 θ
C) sec θ csc θ
D) sin θ tan θ
Use the fundamental identities to simplify the expression.
csc θ cot θ
43)
sec θ
A) sec 2 θ
43)
C) cot2 θ
B) 1
D) csc2 θ
Find the area of triangle ABC with the given parts.
44) A = 29.4°
b = 11.0 in
c = 8.4 in
A) 40 in 2
44)
B) 42 in2
C) 21 in 2
8
D) 23 in2