Uploaded by Kaye Tahum

# Module-1 Lesson-3 Quiz-and-Assignment

```TAHUM, KAYE S.
MATH 3A
Quiz. (2 pts. each)
Direction. Solve for this following.
5π 180&deg;
1. sin (5π/6)= sin( 6 ∗ π )
5 180&deg;
= sin( ∗
)
6
1
900
= sin(
&deg;)
6
= sin(150&deg;)
𝟏
=
𝟐
5π 180&deg;
2. cos (5π/4)= cos( 4 ∗ π )
5 180&deg;
= cos( ∗
)
4
1
900
= cos(
&deg;)
4
= cos(225&deg;)
√𝟐
= −
𝟐
π
180&deg;
3. sin (π/4)= sin( 4 ∗ π )
1 180&deg;
= sin( ∗
)
4
1
180
= sin(
&deg;)
4
= sin(45&deg;)
√𝟐
=
𝟐
π
180&deg;
4. cos (π/4)= cos( 4 ∗ π )
1 180&deg;
= cos( ∗
)
4
1
180
= cos(
&deg;)
4
= cos(150&deg;)
√𝟑
= −
𝟐
11π
180&deg;
5. sin (11π/6)= sin(
∗
)
6
π
11 180&deg;
= sin( ∗
)
6
1
1980
= sin(
&deg;)
6
= sin(330&deg;)
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&deg;
Solution
π
45&deg; = 45&deg; (180&deg;)
π
)
180
45π 45
=
&divide;
180 45
𝛑
𝟒𝟓&deg; =
𝟒
= 45 (
2. 76&deg;
Solution
3. 510&deg;
Solution
π
76&deg; = 76&deg; (
)
180&deg;
π
= 76 (
)
180
76π 4
=
&divide;
180 4
𝟏𝟗𝛑
𝟕𝟔&deg; =
𝟒𝟓
π
4. −240&deg;
Solution
510&deg; = 510&deg; (180&deg;)
π
= 510 (
)
180
510π 30
=
&divide;
180 30
𝟏𝟕𝛑
𝟓𝟏𝟎&deg; =
𝟔
π
−240 = −240&deg; (180&deg;)
π
= −240 (
)
180
240π 60
= −
&divide;
180
60
𝟒𝛑
−𝟐𝟒𝟎&deg; = −
𝟑
5. 0&deg;
Solution
π
0&deg; = 0&deg; (180&deg;)
π
= 0(
)
180
𝟎&deg; = 𝟎
6. 150&deg;
Solution
π
150&deg; = 150&deg; (180&deg;)
π
= 150 (
)
180
150π 30
=
&divide;
180 30
𝟓𝛑
𝟏𝟓𝟎&deg; =
𝟔
7. 40&deg;
Solution
π
8. 270&deg;
Solution
40&deg; = 40&deg; (180&deg;)
π
= 40 (
)
180
40π 20
=
&divide;
180 20
𝟐𝛑
𝟒𝟎&deg; =
𝟗
π
9. 120&deg;
Solution
270&deg; = 270&deg; (180&deg;)
π
= 270 (
)
180
270π 90
=
&divide;
180 90
𝟑𝛑
𝟐𝟕𝟎&deg; =
𝟐
π
120&deg; = 120&deg; (180&deg;)
π
= 120 (
)
180
120π 60
=
&divide;
180 60
𝟐𝛑
𝟏𝟐𝟎&deg; =
𝟑
10. 10&deg;
Solution
π
10&deg; = 10&deg; (180&deg;)
π
= 10 (
)
180
10π 10
=
&divide;
180 10
𝛑
𝟏𝟎&deg; =
𝟏𝟖
11. 50&deg;
Solution
π
12. −30&deg;
Solution
50&deg; = 50&deg; (180&deg;)
π
= 50 (
)
180
50π 10
=
&divide;
180 10
𝟓𝛑
𝟓𝟎&deg; =
𝟏𝟖
π
−30&deg; = −30&deg; (180&deg;)
π
= −30 (
)
180
30π 30
= −
&divide;
180 30
−𝟑𝟎&deg; =
13. 6&deg;
𝛑
𝟔
Solution
π
14. 300&deg;
Solution
6&deg; = 6&deg; (180&deg;)
π
= 6(
)
180
6π 6
=
&divide;
180 6
𝛑
𝟔&deg; =
𝟑𝟎
π
15. −24&deg;
Solution
300&deg; = 300&deg; (180&deg;)
π
= 300 (
)
180
300π 60
=
&divide;
180 60
𝟓𝛑
𝟑𝟎𝟎&deg; =
𝟑
π
−24&deg; = −24&deg; (180&deg;)
π
= −24 (
)
180
24π 12
= −
&divide;
180 12
𝟐𝛑
−𝟐𝟒&deg; =
𝟏𝟓
Convert the following radians measure into degrees.
16.
7𝜋
3
Solution:
7𝜋
3
17.
𝜋
=
7𝜋 180&deg;
( 𝜋 )
7 180&deg;
= (
)
3 1
1,260&deg; 3
=
&divide;
3
3
𝟕𝝅
= 𝟒𝟐𝟎
𝟑
3
6
Solution:
𝜋 𝜋 180&deg;
= (
)
6 6 𝜋
1 180&deg;
= (
)
6 1
180&deg; 6
=
&divide;
6
6
𝝅
= 𝟑𝟎&deg;
𝟔
𝜋
18. 18
Solution:
19.
π
π 180&deg;
=
(
)
18 18 π
1 180&deg;
=
(
)
18 1
180&deg; 18
=
&divide;
18
18
𝝅
= 𝟏𝟎&deg;
𝟏𝟖
𝟑𝝅
𝟒
Solution:
20. −
3π 3π 180&deg;
=
(
)
4
4
π
3 180&deg;
= (
)
4 1
540&deg; 4
=
&divide;
4
4
𝟑𝝅
= 𝟏𝟑𝟓&deg;
𝟒
13π
4
Solution:
−
21. 𝜋
13π
13π 180&deg;
=−
(
)
4
4
π
13 180&deg;
=− (
)
4
1
2,340&deg; 4
=−
&divide;
4
4
𝟏𝟑𝝅
−
= −𝟓𝟖𝟓&deg;
𝟒
Solution:
180&deg;
)
π
180&deg;
=(
)
1
𝝅 = 𝟏𝟖𝟎&deg;
𝜋 = π(
22.
7π
4
Solution:
7π 7π 180&deg;
=
(
)
4
4
π
7 180&deg;
= (
)
4 1
1,260&deg; 4
=
&divide;
4
4
𝟕𝝅
= 𝟑𝟏𝟓&deg;
𝟒
24. 2π
Solution:
180&deg;
2𝜋 = 2π (
)
π
180&deg;
= 2(
)
1
𝟐𝝅 = 𝟑𝟔𝟎&deg;
π
25. 3
Solution:
26.
π π 180&deg;
= (
)
3 3 π
1 180&deg;
= (
)
3 1
180&deg; 3
=
&divide;
3
3
𝝅
= 𝟔𝟎&deg;
𝟑
2π
3
Solution:
2π 2π 180&deg;
=
(
)
3
3
π
2 180&deg;
= (
)
3 1
360&deg; 3
=
&divide;
3
3
𝟐𝝅
= 𝟏𝟐𝟎&deg;
𝟑
π
27. − 4
Solution:
−
π
π 180&deg;
=− (
)
4
4 π
1 180&deg;
=− (
)
4 1
180&deg; 4
=−
&divide;
4
4
𝝅
− = −𝟒𝟓&deg;
𝟒
28. 0
Solution:
180&deg;
0 = 0(
)
π
𝟎 = 𝟎&deg;
29.
5π
4
Solution:
5π 5π 180&deg;
=
(
)
4
4
π
5 180&deg;
= (
)
4 1
900&deg; 4
=
&divide;
4
4
𝟓𝝅
= 𝟐𝟐𝟓&deg;
𝟒
30. 3π
Solution:
180&deg;
)
π
180&deg;
= 3(
)
1
𝟑𝝅 = 𝟓𝟒𝟎&deg;
3π = 3π (
```