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標題:
發問:
Given sin 30 degree = 0.5. Find sin 15 degree in surd form.
最佳解答:
As sin 30 = 1/2, therefore, cos 30 = (√3)/2, that is 2 cos 30 = √3Since cos 30 = 1 - 2 (sin 15)^2, so, 2 cos 30 = 2 - 4 (sin 15)^2==> (2 sin 15)^2 = 2 - 2 cos 30==> (2 sin 15)^2 = 2 - √3==> (2 sin 15)^2 = (√3/√2)^2 - √3 + (1/√2)^2==> (2 sin 15)^2 = (√3/√2 - 1/√2)^2As sin 15 is positive, therefore2 sin 15 = √3/√2 - 1/√2 = (√6 - √2)/2So, sin 15 = (√6 - √2)/4
其他解答:
sin(45°-30°) =sin45°cos30° - cos45°sin30° =(6^0.5-2^0.5)/4
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Maths發問:
Given sin 30 degree = 0.5. Find sin 15 degree in surd form.
最佳解答:
As sin 30 = 1/2, therefore, cos 30 = (√3)/2, that is 2 cos 30 = √3Since cos 30 = 1 - 2 (sin 15)^2, so, 2 cos 30 = 2 - 4 (sin 15)^2==> (2 sin 15)^2 = 2 - 2 cos 30==> (2 sin 15)^2 = 2 - √3==> (2 sin 15)^2 = (√3/√2)^2 - √3 + (1/√2)^2==> (2 sin 15)^2 = (√3/√2 - 1/√2)^2As sin 15 is positive, therefore2 sin 15 = √3/√2 - 1/√2 = (√6 - √2)/2So, sin 15 = (√6 - √2)/4
其他解答:
sin(45°-30°) =sin45°cos30° - cos45°sin30° =(6^0.5-2^0.5)/4
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