TAHUM, KAYE S.
MATH 3A
Quiz. (2 pts. each)
Direction. Solve for this following.
5π 180°
1. sin (5π/6)= sin( 6 ∗ π )
5 180°
= sin( ∗
)
6
1
900
= sin(
°)
6
= sin(150°)
𝟏
=
𝟐
5π 180°
2. cos (5π/4)= cos( 4 ∗ π )
5 180°
= cos( ∗
)
4
1
900
= cos(
°)
4
= cos(225°)
√𝟐
= −
𝟐
π
180°
3. sin (π/4)= sin( 4 ∗ π )
1 180°
= sin( ∗
)
4
1
180
= sin(
°)
4
= sin(45°)
√𝟐
=
𝟐
π
180°
4. cos (π/4)= cos( 4 ∗ π )
1 180°
= cos( ∗
)
4
1
180
= cos(
°)
4
= cos(150°)
√𝟑
= −
𝟐
11π
180°
5. sin (11π/6)= sin(
∗
)
6
π
11 180°
= sin( ∗
)
6
1
1980
= sin(
°)
6
= sin(330°)
𝟏
= −
𝟐
Assignment.
Plot the missing elements of a unit circle. Write it on a short bond paper.
Application
Convert the following degree measure into radians.
1. 45°
Solution
π
45° = 45° (180°)
π
)
180
45π 45
=
÷
180 45
𝛑
𝟒𝟓° =
𝟒
= 45 (
2. 76°
Solution
3. 510°
Solution
π
76° = 76° (
)
180°
π
= 76 (
)
180
76π 4
=
÷
180 4
𝟏𝟗𝛑
𝟕𝟔° =
𝟒𝟓
π
4. −240°
Solution
510° = 510° (180°)
π
= 510 (
)
180
510π 30
=
÷
180 30
𝟏𝟕𝛑
𝟓𝟏𝟎° =
𝟔
π
−240 = −240° (180°)
π
= −240 (
)
180
240π 60
= −
÷
180
60
𝟒𝛑
−𝟐𝟒𝟎° = −
𝟑
5. 0°
Solution
π
0° = 0° (180°)
π
= 0(
)
180
𝟎° = 𝟎
6. 150°
Solution
π
150° = 150° (180°)
π
= 150 (
)
180
150π 30
=
÷
180 30
𝟓𝛑
𝟏𝟓𝟎° =
𝟔
7. 40°
Solution
π
8. 270°
Solution
40° = 40° (180°)
π
= 40 (
)
180
40π 20
=
÷
180 20
𝟐𝛑
𝟒𝟎° =
𝟗
π
9. 120°
Solution
270° = 270° (180°)
π
= 270 (
)
180
270π 90
=
÷
180 90
𝟑𝛑
𝟐𝟕𝟎° =
𝟐
π
120° = 120° (180°)
π
= 120 (
)
180
120π 60
=
÷
180 60
𝟐𝛑
𝟏𝟐𝟎° =
𝟑
10. 10°
Solution
π
10° = 10° (180°)
π
= 10 (
)
180
10π 10
=
÷
180 10
𝛑
𝟏𝟎° =
𝟏𝟖
11. 50°
Solution
π
12. −30°
Solution
50° = 50° (180°)
π
= 50 (
)
180
50π 10
=
÷
180 10
𝟓𝛑
𝟓𝟎° =
𝟏𝟖
π
−30° = −30° (180°)
π
= −30 (
)
180
30π 30
= −
÷
180 30
−𝟑𝟎° =
13. 6°
𝛑
𝟔
Solution
π
14. 300°
Solution
6° = 6° (180°)
π
= 6(
)
180
6π 6
=
÷
180 6
𝛑
𝟔° =
𝟑𝟎
π
15. −24°
Solution
300° = 300° (180°)
π
= 300 (
)
180
300π 60
=
÷
180 60
𝟓𝛑
𝟑𝟎𝟎° =
𝟑
π
−24° = −24° (180°)
π
= −24 (
)
180
24π 12
= −
÷
180 12
𝟐𝛑
−𝟐𝟒° =
𝟏𝟓
Convert the following radians measure into degrees.
16.
7𝜋
3
Solution:
7𝜋
3
17.
𝜋
=
7𝜋 180°
( 𝜋 )
7 180°
= (
)
3 1
1,260° 3
=
÷
3
3
𝟕𝝅
= 𝟒𝟐𝟎
𝟑
3
6
Solution:
𝜋 𝜋 180°
= (
)
6 6 𝜋
1 180°
= (
)
6 1
180° 6
=
÷
6
6
𝝅
= 𝟑𝟎°
𝟔
𝜋
18. 18
Solution:
19.
π
π 180°
=
(
)
18 18 π
1 180°
=
(
)
18 1
180° 18
=
÷
18
18
𝝅
= 𝟏𝟎°
𝟏𝟖
𝟑𝝅
𝟒
Solution:
20. −
3π 3π 180°
=
(
)
4
4
π
3 180°
= (
)
4 1
540° 4
=
÷
4
4
𝟑𝝅
= 𝟏𝟑𝟓°
𝟒
13π
4
Solution:
−
21. 𝜋
13π
13π 180°
=−
(
)
4
4
π
13 180°
=− (
)
4
1
2,340° 4
=−
÷
4
4
𝟏𝟑𝝅
−
= −𝟓𝟖𝟓°
𝟒
Solution:
180°
)
π
180°
=(
)
1
𝝅 = 𝟏𝟖𝟎°
𝜋 = π(
22.
7π
4
Solution:
7π 7π 180°
=
(
)
4
4
π
7 180°
= (
)
4 1
1,260° 4
=
÷
4
4
𝟕𝝅
= 𝟑𝟏𝟓°
𝟒
24. 2π
Solution:
180°
2𝜋 = 2π (
)
π
180°
= 2(
)
1
𝟐𝝅 = 𝟑𝟔𝟎°
π
25. 3
Solution:
26.
π π 180°
= (
)
3 3 π
1 180°
= (
)
3 1
180° 3
=
÷
3
3
𝝅
= 𝟔𝟎°
𝟑
2π
3
Solution:
2π 2π 180°
=
(
)
3
3
π
2 180°
= (
)
3 1
360° 3
=
÷
3
3
𝟐𝝅
= 𝟏𝟐𝟎°
𝟑
π
27. − 4
Solution:
−
π
π 180°
=− (
)
4
4 π
1 180°
=− (
)
4 1
180° 4
=−
÷
4
4
𝝅
− = −𝟒𝟓°
𝟒
28. 0
Solution:
180°
0 = 0(
)
π
𝟎 = 𝟎°
29.
5π
4
Solution:
5π 5π 180°
=
(
)
4
4
π
5 180°
= (
)
4 1
900° 4
=
÷
4
4
𝟓𝝅
= 𝟐𝟐𝟓°
𝟒
30. 3π
Solution:
180°
)
π
180°
= 3(
)
1
𝟑𝝅 = 𝟓𝟒𝟎°
3π = 3π (