匿名使用者
匿名使用者 發問時間: 科學數學 · 4 年前

已知sin20.1度=0.3437,sin20.2度=0.3453,試估計sin20度10分?

1 個解答

評分
  • 4 年前
    最佳解答

    sin20°6' = 20.1° = 0.3437 , sin20°12' = sin20.2° = 0.3453

    sin 3(20°10') = sin (20°6' + 2(20°12'))

    sin 3(20°10') = sin 20°6' cos 2(20°12') + cos 20°6' sin 2(20°12')

    sin 3(20°10') = sin 20°6' (1 - 2sin²20°12') + cos 20°6' * 2sin 20°12' cos 20°12'

    sin 3(20°10') = 0.3437 (1 - 2 * 0.3453²) + √(1 - 0.3437²) * 2 * 0.3453 √(1 - 0.3453²)

    sin 3(20°10') = 0.870378719

    3sin 20°10' - 4sin³20°10' = 0.870378719

    令 x = sin 20°10' , 則 4x³ - 3x + 0.870378719 = 0

    令 f(x) = 4x³ - 3x + 0.870378719 ,

    則 f(0.3437) > 0 > f(0.3453) , (0.3437 + 0.3453)/2 = 0.3445 ,

    f(0.3445) > 0 > f(0.3453) , (0.3445 + 0.3453)/2 = 0.3449 ,

    f(0.3445) > 0 > f(0.3449) , (0.3445 + 0.3449)/2 = 0.3447 ,

    f(0.3447) > 0 > f(0.3449) , (0.3447 + 0.3449)/2 = 0.3448 ,

    f(0.3447) > 0 > f(0.3448) , (0.3447 + 0.3448)/2 = 0.34475 ,

    f(0.34475) > 0 > f(0.3448)

    0.34475 < x < 0.3448

    故 sin 20°10' = 0.3448.

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