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Precalculus
6.1-6.3 Practice Problems
Name___________________________________
SHORT ANSWER. Answer the question. SHOW ALL
APPROPRIATE WORK!
If A denotes the area of the sector of a circle of radius r
formed by the central angle θ, find the missing quantity.
If necessary, round the answer to two decimal places.
!
10) θ =
radians, A = 62 square meters, r = ?
6
Draw the angle.
1) 135°
2) - 3!
4
Solve the problem.
11) A gear with a radius of 8 centimeters is
turning at ! radians/sec. What is the linear
3
Convert the angle to a decimal in degrees. Round the
answer to two decimal places.
3) 75°56'51''
speed at a point on the outer edge of the
gear?
Convert the angle to D° M' S'' form. Round the answer to
the nearest second.
4) 51.46 °
In the problem, t is a real number and P = (x, y) is the
point on the unit circle that corresponds to t. Find the
exact value of the indicated trigonometric function of t.
12) ( 4 ,
9
If s denotes the length of the arc of a circle of radius r
subtended by a central angle θ, find the missing
quantity.
5) r = 15.0 inches, θ = 30°, s = ?
65 )
9
Find tan t.
Find the exact value. Do not use a calculator.
13) sin 2!
Solve the problem.
6) For a circle of radius 4 feet, find the arc length
s subtended by a central angle of 60 °. Round
to the nearest hundredth.
14) tan !
15) cot 3!
2
7) The minute hand of a clock is 5 inches long.
How far does the tip of the minute hand
move in 55 minutes? If necessary, round the
answer to two decimal places.
16) sin (- ! )
2
Convert the angle in degrees to radians. Express the
answer as multiple of ".
8) 160°
17) cos (-!)
18) sec !
4
Convert the angle in radians to degrees.
8!
9)
9
Find the exact value of the expression if θ = 45°. Do not
use a calculator.
19) f(θ) = cos θ
Find 11f(θ).
Find the exact value. Do not use a calculator.
20) cos 60 °
1
Solve the problem.
35) If sin θ = 0.8 , find the value of sin θ + sin (θ +
2!) + sin (θ + 4!).
21) sec !
3
Find the exact value of the expression if θ = 30°. Do not
use a calculator.
22) g(θ) = cos θ
Find g(2θ).
23) f(θ) = cos θ
Name the quadrant in which the angle θ lies.
36) tan θ > 0, sin θ < 0
37) cot θ < 0,
Find 3f(θ).
cos θ > 0
Find the exact value of the expression if θ = 60°. Do not
use a calculator.
24) f(θ) = sin θ
Find 4f(θ).
Use the properties of the trigonometric functions to find
the exact value of the expression. Do not use a calculator.
38) sec2 70° - tan2 70°
Find the exact value. Do not use a calculator.
25) cos 14!
3
Find the exact value of the indicated trigonometric
function of θ.
39) csc θ = - 7 , θ in quadrant III Find cot θ.
4
26) sin 495°
Find the exact value of the expression. Do not use a
calculator.
27) tan 7! + tan 5!
4
4
40) cos θ = 21 , 3! < θ < 2!
29
2
Find cot θ.
41) sin θ = 1 , sec θ < 0
2
Find cos θ
and tan θ.
28) cos 120 ° tan 60°
Use the even-odd properties to find the exact value of
the expression. Do not use a calculator.
42) sin (-60°)
A point on the terminal side of an angle θ is given. Find
the exact value of the indicated trigonometric function of
θ.
29) (-4, 3)
Find sin θ.
Solve the problem.
43) If f(θ) = sin θ and f(a) =
30) (- 1 , 1 )
2 5
Find cos θ.
31) (-4, -1)
Find csc θ.
value of f(-a).
Solve the problem.
32) If sin θ = 0.7, find sin (θ + !).
33) What is the domain of the cosine function?
Use the fact that the trigonometric functions are periodic
to find the exact value of the expression. Do not use a
calculator.
34) tan 570°
2
1
, find the exact
3
Answer Key
Testname: 6.1-6.3 PRACTICE16
1)
2)
3)
4)
5)
6)
7)
75.95 °
51°27'36''
7.9 in.
4.19 ft
28.8 in.
8!
8)
9
9) 160°
10) 15.39 m
8! cm/sec
11)
3
65
4
12)
13)
14)
15)
16)
17)
18)
19)
20)
0
0
0
-1
-1
2
11
2
2
1
2
21) 2
1
22)
2
23)
3
3
2
24) 2
3
25) - 1
2
3
Answer Key
Testname: 6.1-6.3 PRACTICE16
2
26)
2
27) 0
3
28) 29)
2
3
5
30) - 5
29
29
31) - 17
32) -0.7
33) all real numbers
3
34)
35)
36)
37)
38)
3
2.4
III
IV
1
39)
33
4
21
40) 20
41) cos θ = 42) -
3 , tan θ = -
2
3
3
3
2
1
43) 3
4