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受欢迎的三角函数 >

solvefor θ,sin(3θ)= 1/2

解答

求解

θ, sin (3 θ) = \frac{1}{2}

解答

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{5 π}{18} + \frac{2 πn}{3}

+1

度数

θ = 1 0^{\circ} + 12 0^{\circ} n, θ = 5 0^{\circ} + 12 0^{\circ} n

求解步骤

sin (3 θ) = \frac{1}{2}

sin (3 θ) = \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}

3 θ = \frac{π}{6} + 2 πn, 3 θ = \frac{5 π}{6} + 2 πn

3 θ = \frac{π}{6} + 2 πn, 3 θ = \frac{5 π}{6} + 2 πn

解

3 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{18} + \frac{2 πn}{3}

3 θ = \frac{π}{6} + 2 πn

两边除以

3

3 θ = \frac{π}{6} + 2 πn

两边除以

3

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

化简

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

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{\frac{π}{6}}{3} + \frac{2 πn}{3} : \frac{π}{18} + \frac{2 πn}{3}

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

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

使用分式法则:

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

= \frac{π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}

解

3 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{18} + \frac{2 πn}{3}

3 θ = \frac{5 π}{6} + 2 πn

两边除以

3

3 θ = \frac{5 π}{6} + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} = \frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3} : \frac{5 π}{18} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{18}

\frac{\frac{5 π}{6}}{3}

使用分式法则:

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

= \frac{5 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{5 π}{18}

= \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{π}{18} + \frac{2 πn}{3}, θ = \frac{5 π}{18} + \frac{2 πn}{3}

作图

流行的例子

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\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

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\frac{2}{π} arccos (m \cdot 1 - 1) = 0

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