Name: ________________________ Class: ___________________ Date: __________
ID: A
10.1 - 10.5 Quiz
1. In a right triangle, θ is an acute angle and csc =
2. Solve
19
. Evaluate the other five trigonometric functions of θ.
18
DEF .
3. Draw an angle that measures 260° in standard position.
4. Draw an angle that measures 700° in standard position.
5. Draw an angle that measures –340° in standard position.
6. Which angle is coterminal with 153°?
a. –27° b. 63° c. –117° d. 513°
7. Which angle is coterminal with 112°?
a. 382° b. –338° c. 832° d. –68°
8. Which angle is coterminal with –186°?
a. –456° b. –96° c. –546° d. –366°
1
Name: ________________________
ID: A
9. Convert 35° to radians.
10. Convert −
π
30
to degrees.
11. Let ÊÁË −10,24 ˆ˜¯ be a point on the terminal side of an angle θ in standard position. Evaluate the six trigonometric
functions of θ.
12. Use the unit circle to evaluate the six trigonometric functions of θ = −450°.
13. Use the unit circle to evaluate the six trigonometric functions of θ = −
3π
.
2
14. Find the reference angle θ ′ for θ = 329°.
15. Evaluate sin 210° without using a calculator.
16. Evaluate cos
4π
without using a calculator.
3
17. Evaluate tan
7π
without using a calculator.
4
4
π
18. Given cos θ = − and < θ < π find the other five trigonometric functions.
5
2
3
3π
19. Given sin θ = − and π < θ <
find the other five trigonometric functions.
2
5
2
Name: ________________________
ID: A
20. A surveyor starts at the edge of a lake, at point A, and measures a 90° angle between B and C, as shown. The
surveyor then walks 95 meters to B and measures an angle of 79° between A and C. Approximately how many
meters wide is the lake between A and C? Round your answer to the nearest hundredth if necessary.
21. Convert
5π
to degrees
3
22. Evaluate the six trigonometric functions of θ.
23. Find the reference angle θ ′ for θ =
7π
.
4
24. Sketch the angle θ = 225°. Then find its reference angle θ ′.
3
ID: A
10.1 - 10.5 Quiz
Answer Section
1. ANS:
sinθ =
18
19
cos θ =
37
19
tan θ =
18 37
37
sec θ =
19 37
37
cot θ =
37
18
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: evaluating trigonometric functions of acute angles | sine | cosine | tangent | cosecant | secant | cotangent
NOT: Example 2
2. ANS:
E = 71°, d ≈ 4.13, f ≈ 12.69
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: solving right triangles
NOT: Example 4
3. ANS:
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
1
ID: A
4. ANS:
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
5. ANS:
6.
7.
8.
9.
PTS: 1
NAT: HSF-TF.A.1
NOT: Example 1
ANS: D
NAT: HSF-TF.A.1
NOT: Example 2
ANS: C
NAT: HSF-TF.A.1
NOT: Example 2
ANS: C
NAT: HSF-TF.A.1
NOT: Example 2
ANS:
7π
rad
36
DIF: Level 1
REF: Algebra 2 Sec. 9.2
KEY: drawing angles in standard position | standard position | measure of an angle
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
KEY: coterminal | finding coterminal angles | coterminal angles
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
KEY: coterminal | finding coterminal angles | coterminal angles
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
KEY: coterminal | finding coterminal angles | coterminal angles
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
2
ID: A
10. ANS:
–6°
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
11. ANS:
12
13
sin θ = , csc θ =
13
12
5
13
cosθ = − , sec θ = −
13
5
12
5
tan θ = − , cot θ = −
5
12
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: trigonometric function | standard position
NOT: Example 1
12. ANS:
sin θ = –1, csc θ = –1
cosθ = 0, sec θ = undefined
tan θ = undefined, cot θ = 0
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: evaluating trigonometric functions of any angle | trigonometric function | unit circle
NOT: Example 2
13. ANS:
sin θ = 1, csc θ = 1
cosθ = 0, sec θ = undefined
tan θ = undefined, cot θ = 0
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: evaluating trigonometric functions of any angle | trigonometric function | unit circle
NOT: Example 2
14. ANS:
31°
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | finding reference angles
NOT: Example 3
15. ANS:
–0.5
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
3
ID: A
16. ANS:
–0.5
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
17. ANS:
–1
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
18. ANS:
5
sec θ = −
4
sin θ =
3
5
, csc θ =
5
3
3
4
tan θ = − , cot θ = −
4
3
PTS: 1
NAT: HSF-TF.C.8
NOT: Example 1
19. ANS:
5
csc θ = −
3
DIF: Level 1
REF: Algebra 2 Sec. 9.7
KEY: trigonometric function | finding trigonometric values
4
5
cos θ = − , sec θ = −
5
4
tan θ =
3
4
, cot θ =
4
3
PTS:
NAT:
NOT:
20. ANS:
1
HSF-TF.C.8
Example 1
488.73 m
DIF: Level 1
REF: Algebra 2 Sec. 9.7
KEY: trigonometric function | finding trigonometric values
PTS:
NAT:
NOT:
21. ANS:
1
DIF: Level 1
REF: Algebra 2 Sec. 9.1
HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: indirect measurement | application
Example 5
300°
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
4
ID: A
22. ANS:
3
5
sin θ = − , csc θ = −
5
3
4
5
cosθ = − , sec θ = −
5
4
3
4
tan θ = , cot θ =
4
3
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: trigonometric function | standard position
NOT: Example 1
23. ANS:
θ′=
π
4
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | finding reference angles
NOT: Example 3
24. ANS:
θ ′ = 45°
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | finding reference angles
NOT: Example 3
5