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

ISBN-10: 0080103111

ISBN-13: 9780080103112

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Sample text

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.

8. sin 3a cos a — cos 3a sin a = sin 2a. 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).

Therefore, 0 = . . , - 30°, 30°, 150°, 210°, 330° Just as in solving algebraic equations, a word of caution is necessary in the solutions of trigonometric equations. Division by any factor that could be zero in an equation will result in the loss of certain solutions. Squaring may introduce extraneous solutions. Checking solutions by substitution in the original equation will identify any extraneous solutions. Multiplication by a factor may also introduce extraneous solutions. This will happen if the factor used for multiplying comes out later in the process of simplification.

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


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