Self-Assessment Solutions

Degrees Versus Radians

1.	The answer is shown in Figure 3.16. Figure 3.16. The solution to question 1.
2.	The answer is shown in Figure 3.17. Figure 3.17. The solution to question 2.
3.	The answer is shown in Figure 3.18. Figure 3.18. The solution to question 3.

4.
5.
6.

7.	135°
8.	60°
9.	72°

Trigonometric Functions

1.	0.7071
2.	–0.5736
3.	–0.7002
4.	sina = = 0.28, cosa = = 0.96, tana = = 0.29
5.	a = 16.26°
6.	–1.4281
7.	2.9238
8.	1.4142

9.	per = 120°, amp = 5
10.	per = 360°, amp = 3
11.	per = 90°, amp = 1
12.	per = 360°, amp = 5
13.	per = 720°, amp = 2
14.	per = 180°, amp = ½

Trigonometric Identities

1.	sin(180°) = 0 and cos(180°) = –1
2.	sin2(180°) + cos2(180°) = 02 + (–1)2 = 1, so it is true for 180°.
3.	tan(30°) = sin(30°)/cos(30°) = 0.5/0.8660 = 0.5774
4.	sin(2a) = sin(a+a) = sinacosa + cosasina
5.	cos(2a) = cosacosa – sinasina = cos2(a) – sin2(a)
6.	Use the sum identity for sine: sin(90°+30°) = sin90°cos 30° + cos90°sin 30° = cos 30° + 0 = 0.8660