急!! Maths一題,Trigonometric eqt

2012-09-23 2:07 am

sin0tan0 + cos0 = 4 / tan0
where 0 < ''飛ter'' ≤ 360

答案 : 61.98 , 118.02 (cor. to 2 d.p.)

*** 0 = 0中間有一劃果個 , 叫咩''飛ter''

thx!!!!!!!!!!!!!!!!!!!!

回答 (1)

micatkie

2012-09-23 4:12 am

✔ 最佳答案

sinθtanθ + cosθ = 4/tanθ

sinθ(sinθ/cosθ) + cosθ = 4/(sinθ/cosθ)

sin²θ/cosθ + cosθ = 4cosθ/sinθ

sin²θ/cosθ + cos²θ/cosθ = 4cosθ/sinθ

(sin²θ + cos²θ)/cosθ = 4cosθ/sinθ

1/cosθ = 4cosθ/sinθ

4cos²θ = sinθ

4(1 - sin²θ) = sinθ

4 - 4sin²θ = sinθ

4sin²θ + sinθ - 4 = 0

sinθ = [-1 ± √(1² + 4*4*4)]/(2*4)

sinθ = (-1 + √65)/8 or sinθ = (-1 - √65)/8 (rejected)

θ = 61.98°, (180-61.98)°

θ = 61.98°, 118.02°

2012-09-22 20:14:28 補充：
sinθ = (-1 - √65)/8
It is rejected as (-1 - √65)/8 < -1
It is impossible for sinθ < -1

參考: micatkie, micatkie

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