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受欢迎的三角函数 >

3sin(θ/4)-3/2 =0,0<= θ<= 2pi

解答

3 sin (\frac{θ}{4}) - \frac{3}{2} = 0, 0 \leq θ \leq 2 π

解答

θ = \frac{2 π}{3}

+1

度数

θ = 12 0^{\circ}

求解步骤

3 sin (\frac{θ}{4}) - \frac{3}{2} = 0, 0 \leq θ \leq 2 π

将

\frac{3}{2}

到右边

3 sin (\frac{θ}{4}) - \frac{3}{2} = 0

两边加上

\frac{3}{2}

3 sin (\frac{θ}{4}) - \frac{3}{2} + \frac{3}{2} = 0 + \frac{3}{2}

化简

3 sin (\frac{θ}{4}) = \frac{3}{2}

3 sin (\frac{θ}{4}) = \frac{3}{2}

两边除以

3

3 sin (\frac{θ}{4}) = \frac{3}{2}

两边除以

3

\frac{3 sin ( \frac{θ}{4} )}{3} = \frac{\frac{3}{2}}{3}

化简

\frac{3 sin ( \frac{θ}{4} )}{3} = \frac{\frac{3}{2}}{3}

化简

\frac{3 sin ( \frac{θ}{4} )}{3} : sin (\frac{θ}{4})

\frac{3 sin ( \frac{θ}{4} )}{3}

数字相除:

\frac{3}{3} = 1

= sin (\frac{θ}{4})

化简

\frac{\frac{3}{2}}{3} : \frac{1}{2}

\frac{\frac{3}{2}}{3}

使用分式法则:

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

= \frac{3}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{3}{6}

约分:

3

= \frac{1}{2}

sin (\frac{θ}{4}) = \frac{1}{2}

sin (\frac{θ}{4}) = \frac{1}{2}

sin (\frac{θ}{4}) = \frac{1}{2}

sin (\frac{θ}{4}) = \frac{1}{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}

\frac{θ}{4} = \frac{π}{6} + 2 πn, \frac{θ}{4} = \frac{5 π}{6} + 2 πn

\frac{θ}{4} = \frac{π}{6} + 2 πn, \frac{θ}{4} = \frac{5 π}{6} + 2 πn

解

\frac{θ}{4} = \frac{π}{6} + 2 πn : θ = \frac{2 π}{3} + 8 πn

\frac{θ}{4} = \frac{π}{6} + 2 πn

在两边乘以

4

\frac{θ}{4} = \frac{π}{6} + 2 πn

在两边乘以

4

\frac{4 θ}{4} = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

化简

\frac{4 θ}{4} = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

化简

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

数字相除:

\frac{4}{4} = 1

= θ

化简

4 \cdot \frac{π}{6} + 4 \cdot 2 πn : \frac{2 π}{3} + 8 πn

4 \cdot \frac{π}{6} + 4 \cdot 2 πn

4 \cdot \frac{π}{6} = \frac{2 π}{3}

4 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 4}{6}

约分:

2

= \frac{2 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 8 πn

= \frac{2 π}{3} + 8 πn

θ = \frac{2 π}{3} + 8 πn

θ = \frac{2 π}{3} + 8 πn

θ = \frac{2 π}{3} + 8 πn

解

\frac{θ}{4} = \frac{5 π}{6} + 2 πn : θ = \frac{10 π}{3} + 8 πn

\frac{θ}{4} = \frac{5 π}{6} + 2 πn

在两边乘以

4

\frac{θ}{4} = \frac{5 π}{6} + 2 πn

在两边乘以

4

\frac{4 θ}{4} = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

化简

\frac{4 θ}{4} = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

化简

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

数字相除:

\frac{4}{4} = 1

= θ

化简

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn : \frac{10 π}{3} + 8 πn

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{6} = \frac{10 π}{3}

4 \cdot \frac{5 π}{6}

分式相乘:

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

= \frac{5 π 4}{6}

数字相乘:

5 \cdot 4 = 20

= \frac{20 π}{6}

约分:

2

= \frac{10 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 8 πn

= \frac{10 π}{3} + 8 πn

θ = \frac{10 π}{3} + 8 πn

θ = \frac{10 π}{3} + 8 πn

θ = \frac{10 π}{3} + 8 πn

θ = \frac{2 π}{3} + 8 πn, θ = \frac{10 π}{3} + 8 πn

在

0 \leq θ \leq 2 π

范围内的解

θ = \frac{2 π}{3}

作图

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