## Download Analytic Trigonometry by William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. PDF

By William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)

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**Additional resources for Analytic Trigonometry**

**Example text**

FUNCTIONS OF SUMS AND RELATED FUNCTIONS tan 2a + tan a r-— = tan 3a 1 — tan 2a tan a 10. tan 2 0 - tan 0 = tan 0 sec 2 0. Λ 9. t 11. csc 0 - cot 0 -tan ( 4 ) sin 2 0 12. — — = tan 0. 1 + cos 2 0 13. sec 2 0 1 - 2 sin2 0 * 14. (sin 0 - cos 0)2 = 1 - sin 2 0. 15. tan 2 0 cot 0 16. 1 - sin 2 0 cos 2 0 2 1 - tan2 0 1 - tan 0 1 + tan 0 ' Solve the following equations for 0 < 0 < 2 π: 17. sin 2 0 = i λ/3" 18. cos 2 0 = - -^- . 19. 1 - 2 sin2 2 0 = h (Show two methods). 20. 2 cos2 0 — 1 = - 2. (Show two methods).

1 - sin 2 0 cos 2 0 2 1 - tan2 0 1 - tan 0 1 + tan 0 ' Solve the following equations for 0 < 0 < 2 π: 17. sin 2 0 = i λ/3" 18. cos 2 0 = - -^- . 19. 1 - 2 sin2 2 0 = h (Show two methods). 20. 2 cos2 0 — 1 = - 2. (Show two methods). 21. sin (2 0 + Ή 22. tan (l 0 - ^ j = 1. Λ= - i 23. (sin 2 0 - 1) (sin 0 + 1) = 0. 24. 2 sin2 ( | ) - 3 sin (JA +1=0. 25. 2 cos2 2 0 + 3 sin 2 0 - 3 = 0 . 26. tan2 2 0 - 2 tan 2 0 + 1 = 0. 27. \ Λ + sin 2 0 = cos 2 0. 28. sin 0 + cos 0 = 1.

Since Θ is a reference angle, it lies somewhere between 0° and 90°. 41098. 41078 sin ? 41098_| Lsin 24° 16' 6 60 Hence, — = —. andFp = , or approximately 2. 2'. 5 Find from Table III: 1. sin 20° 17' 4. cot 51° 53' 2. tan 42° 11' 5. tan 11° 22' 3. cos 60° 39' 6. sin 77° 17' Interpolate to find the value of each from Table III: 8. 7' 7. 6' 9. 3' 10. 8' 11. 6' 12. 1' 13. 7' 14. 7' Find the reference angle Θ from Table III: 15. 41204 16. 61160 17. 36894 18. 48521 Interpolate to find the reference angle 0 from Table III: 19.