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. | Trigonometric Functions | | | | 1. | 0.7071 | | | | | 2. | “0.5736 | | | | | 3. | “0.7002 | | | | | 4. | sin a = = 0.28, cos a = = 0.96, tan a = = 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. | sin 2 (180 °) + cos 2 (180 °) = 0 2 + ( “1) 2 = 1, so it is true for 180 °. | | | | | 3. | tan(30 °) = sin(30 °)/cos(30 °) = 0.5/0.8660 = 0.5774 | | | | | 4. | sin(2 a ) = sin( a + a ) = sin a cos a + cos a sin a | | | | | 5. | cos(2 a ) = cos a cos a “ sin a sin a = cos 2 ( a ) “ sin 2 ( a ) | | | | | 6. | Use the sum identity for sine: sin(90 °+30 °) = sin90 °cos 30 ° + cos90 °sin 30 ° = cos 30 ° + 0 = 0.8660 | |