在三角函数中,角度的单位一般以弧度表示。
因此,我们需要将角度转换为弧度才能计算三角函数的值。角度和弧度的转换关系是:
1、度 = π/180弧度由此可得;30度 = (π/180) * 30 = π/6 弧度。然后,我们可以计算30度到360度范围内的三角函数值:- 正弦函数(sin):sin(30°) = sin(π/6) ≈ 0.5sin(60°) = sin(π/3) ≈ 0.866sin(90°) = sin(π/2) = 1sin(120°) = sin(2π/3) ≈ 0.866sin(150°) = sin(5π/6) ≈ 0.5sin(180°) = sin(π) = 0sin(210°) = sin(7π/6) ≈ -0.5sin(240°) = sin(4π/3) ≈ -0.866sin(270°) = sin(3π/2) = -1sin(300°) = sin(5π/3) ≈ -0.866sin(330°) = sin(11π/6) ≈ -0.5- 余弦函数(cos):cos(30°) = cos(π/6) ≈ 0.866cos(60°) = cos(π/3) ≈ 0.5cos(90°) = cos(π/2) = 0cos(120°) = cos(2π/3) ≈ -0.5cos(150°) = cos(5π/6) ≈ -0.866cos(180°) = cos(π) = -1cos(210°) = cos(7π/6) ≈ -0.866cos(240°) = cos(4π/3) ≈ -0.5cos(270°) = cos(3π/2) = 0cos(300°) = cos(5π/3) ≈ 0.5cos(330°) = cos(11π/6) ≈ 0.866- 正切函数(tan):tan(30°) = tan(π/6) ≈ 0.577tan(60°) = tan(π/3) ≈ 1.732tan(90°) = tan(π/2) = 无穷大tan(120°) = tan(2π/3) ≈ -1.732tan(150°) = tan(5π/6) ≈ -0.577tan(180°) = tan(π) = 0tan(210°) = tan(7π/6) ≈ 0.577tan(240°) = tan(4π/3) ≈ 1.732tan(270°) = tan(3π/2) = 无穷大tan(300°) = tan(5π/3) ≈ -1.732tan(330°) = tan(11π/6) ≈ -0.577这些是30度到360度范围内的三角函数值的近似结果。请注意,由于计算的精度限制,所给结果可能有一定的舍入误差。