Analytic

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

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

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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.

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