TAHUM, KAYE S.
BSED MATH 3A
MATH 14: TRIGONOMETRY
QUIZ
What are the degrees of a circle?
 Whole circle is equal to 360 degrees, half of it is equal to 180 degrees and half of the half
of the circle is equal to 90 degrees which we called right-angle.
How about the semicircle?
 Semicircle is half of the whole circle which has 180 degrees.
What are the names of the two forms of the sides on an angle?
 Initial side and Terminal side.
Give an example of an angle in a real-life object and its degrees.
 Scissor − 𝟔𝟎°
 Windmill − 𝟏𝟓𝟎°
 Windows − 𝟗𝟎°
Assignment
Instruction: Give 3 examples on an angle that we can see in the school and draw or print that figure
inside the unit circle along with its degrees.
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
π
76° = 76° (
)
180°
π
= 76 (
)
180
76π 4
=
÷
180 4
𝟏𝟗𝛑
𝟕𝟔° =
𝟒𝟓
3. 510°
Solution
π
510° = 510° (180°)
π
= 510 (
)
180
510π 30
=
÷
180
30
𝟏𝟕𝛑
𝟓𝟏𝟎° =
𝟔
4. −240°
Solution
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
)
180
= 150 (
=
150π 30
÷
180
30
𝟏𝟓𝟎° =
𝟓𝛑
𝟔
7. 40°
Solution
π
40° = 40° (180°)
π
)
180
= 40 (
=
40π 20
÷
180 20
𝟐𝛑
𝟗
𝟒𝟎° =
8. 270°
Solution
π
270° = 270° (180°)
π
)
180
= 270 (
=
270π 90
÷
180
90
𝟐𝟕𝟎° =
𝟑𝛑
𝟐
9. 120°
Solution
π
120° = 120° (180°)
π
)
180
= 120 (
=
120π 60
÷
180
60
𝟏𝟐𝟎° =
𝟐𝛑
𝟑
10. 10°
Solution
π
10° = 10° (180°)
π
)
180
= 10 (
10π 10
÷
180 10
𝛑
𝟏𝟎° =
𝟏𝟖
=
11. 50°
Solution
π
50° = 50° (180°)
π
)
180
= 50 (
=
50π 10
÷
180 10
𝟓𝟎° =
𝟓𝛑
𝟏𝟖
12. −30°
Solution
π
−30° = −30° (180°)
= −30 (
= −
π
)
180
30π 30
÷
180 30
𝛑
𝟔
−𝟑𝟎° =
13. 6°
Solution
π
6° = 6° (180°)
= 6(
π
)
180
6π 6
÷
180 6
𝛑
𝟔° =
𝟑𝟎
=
14. 300°
Solution
π
300° = 300° (180°)
π
)
180
= 300 (
=
300π 60
÷
180
60
𝟑𝟎𝟎° =
𝟓𝛑
𝟑
15. −24°
Solution
π
−24° = −24° (180°)
= −24 (
= −
π
)
180
24π 12
÷
180 12
−𝟐𝟒° =
𝟐𝛑
𝟏𝟓
Convert the following radians measure into degrees.
16.
7𝜋
3
Solution:
7𝜋
3
=
7𝜋 180°
( 𝜋 )
7 180°
= (
)
3 1
1,260° 3
=
÷
3
3
3
𝟕𝝅
= 𝟒𝟐𝟎
𝟑
𝜋
17. 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:
−
13π
13π 180°
=−
(
)
4
4
π
13 180°
=− (
)
4
1
2,340° 4
=−
÷
4
4
𝟏𝟑𝝅
−
= −𝟓𝟖𝟓°
𝟒
21. 𝜋
Solution:
180°
𝜋 = π(
)
π
180°
=(
)
1
𝝅 = 𝟏𝟖𝟎°
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°
)
π
180°
= 2(
)
1
𝟐𝝅 = 𝟑𝟔𝟎°
2𝜋 = 2π (
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°
3π = 3π (
)
π
180°
= 3(
)
1
𝟑𝝅 = 𝟓𝟒𝟎°