標題:
Compound angle EX.
發問:
If 36cos^2 x-3sinx=31 and 90degrees<180degrees, find the value of sin2x.
最佳解答:
36 cos2 x - 3 sin x = 31 36(1 - sin2 x) - 3 sin x = 31 -36 sin2 x - 3 sin x + 5 = 0 (- 12 sin x + 5) (3 sin x - 1) = 0 sin x = -5/12 (rejected) or 1/3 cos2 x = 1 - (1/3)2 = 8/9 cos x = - 2√2/3 (∵ 90° < x < 180°) sin 2x = 2 sin x cos x = 2 (1/3) (- 2√2/3) = -4√2/9
Compound angle EX.
發問:
If 36cos^2 x-3sinx=31 and 90degrees<180degrees, find the value of sin2x.
最佳解答:
36 cos2 x - 3 sin x = 31 36(1 - sin2 x) - 3 sin x = 31 -36 sin2 x - 3 sin x + 5 = 0 (- 12 sin x + 5) (3 sin x - 1) = 0 sin x = -5/12 (rejected) or 1/3 cos2 x = 1 - (1/3)2 = 8/9 cos x = - 2√2/3 (∵ 90° < x < 180°) sin 2x = 2 sin x cos x = 2 (1/3) (- 2√2/3) = -4√2/9
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