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受欢迎的三角函数 >

sin(θ+pi/4)=0

解答

sin (θ + \frac{π}{4}) = 0

解答

θ = 2 πn - \frac{π}{4}, θ = π + 2 πn - \frac{π}{4}

+1

度数

θ = - 4 5^{\circ} + 36 0^{\circ} n, θ = 13 5^{\circ} + 36 0^{\circ} n

求解步骤

sin (θ + \frac{π}{4}) = 0

sin (θ + \frac{π}{4}) = 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 + \frac{π}{4} = 0 + 2 πn, θ + \frac{π}{4} = π + 2 πn

θ + \frac{π}{4} = 0 + 2 πn, θ + \frac{π}{4} = π + 2 πn

解

θ + \frac{π}{4} = 0 + 2 πn : θ = 2 πn - \frac{π}{4}

θ + \frac{π}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

θ + \frac{π}{4} = 2 πn

将

\frac{π}{4}

到右边

θ + \frac{π}{4} = 2 πn

两边减去

\frac{π}{4}

θ + \frac{π}{4} - \frac{π}{4} = 2 πn - \frac{π}{4}

化简

θ = 2 πn - \frac{π}{4}

θ = 2 πn - \frac{π}{4}

解

θ + \frac{π}{4} = π + 2 πn : θ = π + 2 πn - \frac{π}{4}

θ + \frac{π}{4} = π + 2 πn

将

\frac{π}{4}

到右边

θ + \frac{π}{4} = π + 2 πn

两边减去

\frac{π}{4}

θ + \frac{π}{4} - \frac{π}{4} = π + 2 πn - \frac{π}{4}

化简

θ = π + 2 πn - \frac{π}{4}

θ = π + 2 πn - \frac{π}{4}

θ = 2 πn - \frac{π}{4}, θ = π + 2 πn - \frac{π}{4}

作图

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