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受欢迎的三角函数 >

solvefor x,2cos((pix)/3)=1

解答

求解

x, 2 cos (\frac{π x}{3}) = 1

解答

x = 1 + 6 n, x = 5 + 6 n

+1

度数

x = 57.29577 \dots^{\circ} + 343.77467 \dots^{\circ} n, x = 286.47889 \dots^{\circ} + 343.77467 \dots^{\circ} n

求解步骤

2 cos (\frac{π x}{3}) = 1

两边除以

2

2 cos (\frac{π x}{3}) = 1

两边除以

2

\frac{2 cos ( \frac{π x}{3} )}{2} = \frac{1}{2}

化简

cos (\frac{π x}{3}) = \frac{1}{2}

cos (\frac{π x}{3}) = \frac{1}{2}

cos (\frac{π x}{3}) = \frac{1}{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 x}{3} = \frac{π}{3} + 2 πn, \frac{π x}{3} = \frac{5 π}{3} + 2 πn

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

解

\frac{π x}{3} = \frac{π}{3} + 2 πn : x = 1 + 6 n

\frac{π x}{3} = \frac{π}{3} + 2 πn

在两边乘以

3

\frac{π x}{3} = \frac{π}{3} + 2 πn

在两边乘以

3

\frac{3 π x}{3} = 3 \cdot \frac{π}{3} + 3 \cdot 2 πn

化简

\frac{3 π x}{3} = 3 \cdot \frac{π}{3} + 3 \cdot 2 πn

化简

\frac{3 π x}{3} : π x

\frac{3 π x}{3}

数字相除:

\frac{3}{3} = 1

= π x

化简

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

3 \cdot \frac{π}{3} + 3 \cdot 2 πn

3 \cdot \frac{π}{3} = π

3 \cdot \frac{π}{3}

分式相乘:

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

= \frac{π 3}{3}

约分:

3

= π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 6 πn

= π + 6 πn

π x = π + 6 πn

π x = π + 6 πn

π x = π + 6 πn

两边除以

π

π x = π + 6 πn

两边除以

π

\frac{π x}{π} = \frac{π}{π} + \frac{6 πn}{π}

化简

\frac{π x}{π} = \frac{π}{π} + \frac{6 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{π}{π} + \frac{6 πn}{π} : 1 + 6 n

\frac{π}{π} + \frac{6 πn}{π}

使用法则

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{6 πn}{π}

消掉

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

约分:

π

= 6 n

= 1 + 6 n

x = 1 + 6 n

x = 1 + 6 n

x = 1 + 6 n

解

\frac{π x}{3} = \frac{5 π}{3} + 2 πn : x = 5 + 6 n

\frac{π x}{3} = \frac{5 π}{3} + 2 πn

在两边乘以

3

\frac{π x}{3} = \frac{5 π}{3} + 2 πn

在两边乘以

3

\frac{3 π x}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

化简

\frac{3 π x}{3} = 3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

化简

\frac{3 π x}{3} : π x

\frac{3 π x}{3}

数字相除:

\frac{3}{3} = 1

= π x

化简

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

3 \cdot \frac{5 π}{3} + 3 \cdot 2 πn

3 \cdot \frac{5 π}{3} = 5 π

3 \cdot \frac{5 π}{3}

分式相乘:

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

= \frac{5 π 3}{3}

约分:

3

= 5 π

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 6 πn

= 5 π + 6 πn

π x = 5 π + 6 πn

π x = 5 π + 6 πn

π x = 5 π + 6 πn

两边除以

π

π x = 5 π + 6 πn

两边除以

π

\frac{π x}{π} = \frac{5 π}{π} + \frac{6 πn}{π}

化简

\frac{π x}{π} = \frac{5 π}{π} + \frac{6 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

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

\frac{5 π}{π} + \frac{6 πn}{π}

消掉

\frac{5 π}{π} : 5

\frac{5 π}{π}

约分:

π

= 5

= 5 + \frac{6 πn}{π}

消掉

\frac{6 πn}{π} : 6 n

\frac{6 πn}{π}

约分:

π

= 6 n

= 5 + 6 n

x = 5 + 6 n

x = 5 + 6 n

x = 5 + 6 n

x = 1 + 6 n, x = 5 + 6 n

作图

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