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受欢迎的三角函数 >

sin(θ)sin(2θ)=0

解答

sin (θ) sin (2 θ) = 0

解答

θ = πn, θ = \frac{π}{2} + πn

+1

度数

θ = 0^{\circ} + 18 0^{\circ} n, θ = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

sin (θ) sin (2 θ) = 0

分别求解每个部分

sin (θ) = 0 or sin (2 θ) = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = 0

sin (θ) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

解

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

sin (2 θ) = 0 : θ = πn, θ = \frac{π}{2} + πn

sin (2 θ) = 0

sin (2 θ) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 θ = 0 + 2 πn, 2 θ = π + 2 πn

2 θ = 0 + 2 πn, 2 θ = π + 2 πn

解

2 θ = 0 + 2 πn : θ = πn

2 θ = 0 + 2 πn

0 + 2 πn = 2 πn

2 θ = 2 πn

两边除以

2

2 θ = 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{2 πn}{2}

化简

θ = πn

θ = πn

解

2 θ = π + 2 πn : θ = \frac{π}{2} + πn

2 θ = π + 2 πn

两边除以

2

2 θ = π + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{2 πn}{2}

化简

θ = \frac{π}{2} + πn

θ = \frac{π}{2} + πn

θ = πn, θ = \frac{π}{2} + πn

合并所有解

θ = 2 πn, θ = π + 2 πn, θ = πn, θ = \frac{π}{2} + πn

合并重叠的区间

θ = πn, θ = \frac{π}{2} + πn

作图

流行的例子

2sin(θ)-sqrt(3)=0