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受欢迎的三角函数 >

2cos(pi/5 θ)=sqrt(3)

解答

2 cos (\frac{π}{5} θ) = 3

解答

θ = \frac{5}{6} + 10 n, θ = \frac{55}{6} + 10 n

+1

度数

θ = 47.74648 \dots^{\circ} + 572.95779 \dots^{\circ} n, θ = 525.21131 \dots^{\circ} + 572.95779 \dots^{\circ} n

求解步骤

2 cos (\frac{π}{5} θ) = 3

两边除以

2

2 cos (\frac{π}{5} θ) = 3

两边除以

2

\frac{2 cos ( \frac{π}{5} θ )}{2} = \frac{3}{2}

化简

cos (\frac{π}{5} θ) = \frac{3}{2}

cos (\frac{π}{5} θ) = \frac{3}{2}

cos (\frac{π}{5} θ) = \frac{3}{2}

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}

\frac{π}{5} θ = \frac{π}{6} + 2 πn, \frac{π}{5} θ = \frac{11 π}{6} + 2 πn

\frac{π}{5} θ = \frac{π}{6} + 2 πn, \frac{π}{5} θ = \frac{11 π}{6} + 2 πn

解

\frac{π}{5} θ = \frac{π}{6} + 2 πn : θ = \frac{5}{6} + 10 n

\frac{π}{5} θ = \frac{π}{6} + 2 πn

在两边乘以

5

\frac{π}{5} θ = \frac{π}{6} + 2 πn

在两边乘以

5

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

化简

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

化简

5 \cdot \frac{π}{5} θ : π θ

5 \cdot \frac{π}{5} θ

分式相乘:

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

= \frac{5 π}{5} θ

约分:

5

= θ π

化简

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

5 \cdot \frac{π}{6} + 5 \cdot 2 πn

乘

5 \cdot \frac{π}{6} : \frac{5 π}{6}

5 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 5}{6}

= \frac{5 π}{6} + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= \frac{5 π}{6} + 10 πn

π θ = \frac{5 π}{6} + 10 πn

π θ = \frac{5 π}{6} + 10 πn

π θ = \frac{5 π}{6} + 10 πn

两边除以

π

π θ = \frac{5 π}{6} + 10 πn

两边除以

π

\frac{π θ}{π} = \frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

化简

\frac{π θ}{π} = \frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

化简

\frac{π θ}{π} : θ

\frac{π θ}{π}

约分:

π

= θ

化简

\frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π} : \frac{5}{6} + 10 n

\frac{\frac{5 π}{6}}{π} + \frac{10 πn}{π}

\frac{\frac{5 π}{6}}{π} = \frac{5}{6}

\frac{\frac{5 π}{6}}{π}

使用分式法则:

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

= \frac{5 π}{6 π}

约分:

π

= \frac{5}{6}

\frac{10 πn}{π} = 10 n

\frac{10 πn}{π}

约分:

π

= 10 n

= \frac{5}{6} + 10 n

θ = \frac{5}{6} + 10 n

θ = \frac{5}{6} + 10 n

θ = \frac{5}{6} + 10 n

解

\frac{π}{5} θ = \frac{11 π}{6} + 2 πn : θ = \frac{55}{6} + 10 n

\frac{π}{5} θ = \frac{11 π}{6} + 2 πn

在两边乘以

5

\frac{π}{5} θ = \frac{11 π}{6} + 2 πn

在两边乘以

5

5 \cdot \frac{π}{5} θ = 5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} θ = 5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

化简

5 \cdot \frac{π}{5} θ : π θ

5 \cdot \frac{π}{5} θ

分式相乘:

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

= \frac{5 π}{5} θ

约分:

5

= θ π

化简

5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn : \frac{55 π}{6} + 10 πn

5 \cdot \frac{11 π}{6} + 5 \cdot 2 πn

5 \cdot \frac{11 π}{6} = \frac{55 π}{6}

5 \cdot \frac{11 π}{6}

分式相乘:

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

= \frac{11 π 5}{6}

数字相乘:

11 \cdot 5 = 55

= \frac{55 π}{6}

5 \cdot 2 πn = 10 πn

5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 10 πn

= \frac{55 π}{6} + 10 πn

π θ = \frac{55 π}{6} + 10 πn

π θ = \frac{55 π}{6} + 10 πn

π θ = \frac{55 π}{6} + 10 πn

两边除以

π

π θ = \frac{55 π}{6} + 10 πn

两边除以

π

\frac{π θ}{π} = \frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

化简

\frac{π θ}{π} = \frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

化简

\frac{π θ}{π} : θ

\frac{π θ}{π}

约分:

π

= θ

化简

\frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π} : \frac{55}{6} + 10 n

\frac{\frac{55 π}{6}}{π} + \frac{10 πn}{π}

\frac{\frac{55 π}{6}}{π} = \frac{55}{6}

\frac{\frac{55 π}{6}}{π}

使用分式法则:

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

= \frac{55 π}{6 π}

约分:

π

= \frac{55}{6}

\frac{10 πn}{π} = 10 n

\frac{10 πn}{π}

约分:

π

= 10 n

= \frac{55}{6} + 10 n

θ = \frac{55}{6} + 10 n

θ = \frac{55}{6} + 10 n

θ = \frac{55}{6} + 10 n

θ = \frac{5}{6} + 10 n, θ = \frac{55}{6} + 10 n

作图

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