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Trigonometric Functions of Acute Angles Worksheet

Trigonometric Functions of Acute Angles Worksheet
  • Page 1
 1.  
What is the value 70° 45′ in decimal form?
a.
70.55°
b.
70.75°
c.
70.85°
d.
70.65°


Solution:

70° 45′ = (70 + 45 / 60)° = 70.75°


Correct answer : (2)
 2.  
Write the value of 102°13′ in decimal form, rounded to four decimal places.
a.
102.0304°
b.
102.5178°
c.
102.9605°
d.
102.2167°


Solution:

102°13′ = (102 + 13 / 60)° = 102.2167°


Correct answer : (4)
 3.  
Find the value of sin 30.35° in decimal form rounded to four decimal places.
a.
0.5053
b.
0.5038
c.
0.5043
d.
0.5000


Solution:

Sin 30.35° = 0.50528088
[Use a calculator.]


Correct answer : (1)
 4.  
What is the value of tan 70.1° rounded to four decimal places?
a.
2.7625
b.
0.7625
c.
2.6625
d.
70.10


Solution:

Tan 70.1° = 2.762469503
[Use a calculator.]


Correct answer : (1)
 5.  
What is the value of Sec 5.25° rounded to four decimal places?
a.
0.1904
b.
5.2500
c.
1.0042
d.
0.9958


Solution:

Sec 5.25° = 1.0042, rounded to four decimal places.
[Use a calculator.]


Correct answer : (3)
 6.  
What is the value of tan π3 rounded to four decimal places?
a.
1.7320
b.
0.5773
c.
1.0472


Solution:

tan π3 = tan (1.047197551) = 1.7320
[Use a calculator.]


Correct answer : (1)
 7.  
Write the value of cos 3π5 rounded to four decimal places.
a.
0.9995
b.
- 0.3249
c.
- 0.3090
d.
0.9945


Solution:

cos 3π5 = cos (1.884955592) = - 0.3090
[Use a calculator.]


Correct answer : (3)
 8.  
What is the value of csc 3π4 rounded to four decimal places?
a.
- 0.7071
b.
0.7071
c.
- 1.4142
d.
1.4159


Solution:

csc 3π4 = csc(2.35619449)
[Use a calculator.]

= 1.4159, rounded to four decimal places.


Correct answer : (4)
 9.  
The value of Sin (- 39° 20′) rounded to four decimal places is:
a.
- 0.6338
b.
0.6320
c.
- 0.6427
d.
0.6338


Solution:

Be sure your calculator is in the degree mode.

Use the Sin key.

Sin (-39°20′) = Sin [- (39 + 20 / 60)]°

= Sin (- 39.33333333)°

= - 0.6338

Note that - 39°20′ + 360° = 320° 40′. Since a - 39° 20′ angle is coterminal with 320°40′ angle, its terminal side is in the fourth quadrant and the sine is negative.


Correct answer : (1)
 10.  
What is the value of cot (- 230° 24′) rounded to four decimal places?
a.
0.7875
b.
- 0.7875
c.
- 0.8273
d.
0.8273


Solution:

cot (- 230° 24′) = cot[- (230 + 24 / 60)°]
[Change minutes into degrees.]

= cot (- 230.4°)

= - 0.8273
[Use a calculator.]


Correct answer : (3)

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