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受欢迎的三角函数 >

sin(2θ)=(sqrt(3))/2 ,0<= θ<2pi

解答

sin (2 θ) = \frac{3}{2}, 0 \leq θ < 2 π

解答

θ = \frac{π}{6}, θ = \frac{π}{3}, θ = \frac{7 π}{6}, θ = \frac{4 π}{3}

+1

度数

θ = 3 0^{\circ}, θ = 6 0^{\circ}, θ = 21 0^{\circ}, θ = 24 0^{\circ}

求解步骤

sin (2 θ) = \frac{3}{2}, 0 \leq θ < 2 π

sin (2 θ) = \frac{3}{2}

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

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

解

2 θ = \frac{π}{3} + 2 πn : θ = \frac{π}{6} + πn

2 θ = \frac{π}{3} + 2 πn

两边除以

2

2 θ = \frac{π}{3} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数字相除:

\frac{2}{2} = 1

= θ

化简

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

解

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

2 θ = \frac{2 π}{3} + 2 πn

两边除以

2

2 θ = \frac{2 π}{3} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数字相除:

\frac{2}{2} = 1

= θ

化简

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{3} + πn

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{2 π}{6}

约分:

2

= \frac{π}{3}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{3} + πn

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

θ = \frac{π}{6} + πn, θ = \frac{π}{3} + πn

在

0 \leq θ < 2 π

范围内的解

θ = \frac{π}{6}, θ = \frac{π}{3}, θ = \frac{7 π}{6}, θ = \frac{4 π}{3}

作图

流行的例子

- sin (4 x) = 0

csc (x) = sec (4 1^{\circ})

sin(x)-sin(3x)=0

sin (x) - sin (3 x) = 0

2sin^2(θ)-5cos(θ)+1=0

2 sin^{2} (θ) - 5 cos (θ) + 1 = 0

sec^2(x)cos(x)=cos(x),0<x<360

sec^{2} (x) cos (x) = cos (x), 0^{\circ} < x < 36 0^{\circ}