sin15°的值等于 0.6502878401571。
计算过程如下:
[ sin(15^circ) = sin(45^circ - 30^circ) = sin(45^circ)cos(30^circ) - cos(45^circ)sin(30^circ) ]
利用特殊角的三角函数值:
[ sin(45^circ) = frac{sqrt{2}}{2}, quad cos(30^circ) = frac{sqrt{3}}{2}, quad cos(45^circ) = frac{sqrt{2}}{2}, quad sin(30^circ) = frac{1}{2} ]
代入公式:
[ sin(15^circ) = left(frac{sqrt{2}}{2}right) left(frac{sqrt{3}}{2}right) - left(frac{sqrt{2}}{2}right) left(frac{1}{2}right) ]
[ sin(15^circ) = frac{sqrt{6}}{4} - frac{sqrt{2}}{4} ]
[ sin(15^circ) = frac{sqrt{6} - sqrt{2}}{4} ]
因此,sin15°的值为0.6502878401571。