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受欢迎的三角函数 >

sin^2(θ)cos^2(θ)=0,0<= θ<2pi

解答

sin^{2} (θ) cos^{2} (θ) = 0, 0 \leq θ < 2 π

解答

θ = 0, θ = π, θ = \frac{π}{2}, θ = \frac{3 π}{2}

+1

度数

θ = 0^{\circ}, θ = 18 0^{\circ}, θ = 9 0^{\circ}, θ = 27 0^{\circ}

求解步骤

sin^{2} (θ) cos^{2} (θ) = 0, 0 \leq θ < 2 π

分别求解每个部分

sin^{2} (θ) = 0 or cos^{2} (θ) = 0

sin^{2} (θ) = 0, 0 \leq θ < 2 π : θ = 0, θ = π

sin^{2} (θ) = 0, 0 \leq θ < 2 π

使用法则

x^{n} = 0 \Rightarrow x = 0

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

在

0 \leq θ < 2 π

范围内的解

θ = 0, θ = π

cos^{2} (θ) = 0, 0 \leq θ < 2 π : θ = \frac{π}{2}, θ = \frac{3 π}{2}

cos^{2} (θ) = 0, 0 \leq θ < 2 π

使用法则

x^{n} = 0 \Rightarrow x = 0

cos (θ) = 0

cos (θ) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

在

0 \leq θ < 2 π

范围内的解

θ = \frac{π}{2}, θ = \frac{3 π}{2}

合并所有解

θ = 0, θ = π, θ = \frac{π}{2}, θ = \frac{3 π}{2}

作图

流行的例子

2sin(2x)+cos(2x)=0

300= 1/32 100^2sin(2x)

sin^2(x)= 45/52