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受欢迎的三角函数 >

cos(pi/6 t)=0

解答

cos (\frac{π}{6} t) = 0

解答

t = 3 + 12 n, t = 9 + 12 n

+1

度数

t = 171.88733 \dots^{\circ} + 687.54935 \dots^{\circ} n, t = 515.66201 \dots^{\circ} + 687.54935 \dots^{\circ} n

求解步骤

cos (\frac{π}{6} t) = 0

cos (\frac{π}{6} t) = 0

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

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

解

\frac{π}{6} t = \frac{π}{2} + 2 πn : t = 3 + 12 n

\frac{π}{6} t = \frac{π}{2} + 2 πn

在两边乘以

6

\frac{π}{6} t = \frac{π}{2} + 2 πn

在两边乘以

6

6 \cdot \frac{π}{6} t = 6 \cdot \frac{π}{2} + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} t = 6 \cdot \frac{π}{2} + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} t : π t

6 \cdot \frac{π}{6} t

分式相乘:

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

= \frac{6 π}{6} t

约分:

6

= t π

化简

6 \cdot \frac{π}{2} + 6 \cdot 2 πn : 3 π + 12 πn

6 \cdot \frac{π}{2} + 6 \cdot 2 πn

6 \cdot \frac{π}{2} = 3 π

6 \cdot \frac{π}{2}

分式相乘:

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

= \frac{π 6}{2}

数字相除:

\frac{6}{2} = 3

= 3 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= 3 π + 12 πn

π t = 3 π + 12 πn

π t = 3 π + 12 πn

π t = 3 π + 12 πn

两边除以

π

π t = 3 π + 12 πn

两边除以

π

\frac{π t}{π} = \frac{3 π}{π} + \frac{12 πn}{π}

化简

\frac{π t}{π} = \frac{3 π}{π} + \frac{12 πn}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{3 π}{π} + \frac{12 πn}{π} : 3 + 12 n

\frac{3 π}{π} + \frac{12 πn}{π}

消掉

\frac{3 π}{π} : 3

\frac{3 π}{π}

约分:

π

= 3

= 3 + \frac{12 πn}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 3 + 12 n

t = 3 + 12 n

t = 3 + 12 n

t = 3 + 12 n

解

\frac{π}{6} t = \frac{3 π}{2} + 2 πn : t = 9 + 12 n

\frac{π}{6} t = \frac{3 π}{2} + 2 πn

在两边乘以

6

\frac{π}{6} t = \frac{3 π}{2} + 2 πn

在两边乘以

6

6 \cdot \frac{π}{6} t = 6 \cdot \frac{3 π}{2} + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} t = 6 \cdot \frac{3 π}{2} + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} t : π t

6 \cdot \frac{π}{6} t

分式相乘:

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

= \frac{6 π}{6} t

约分:

6

= t π

化简

6 \cdot \frac{3 π}{2} + 6 \cdot 2 πn : 9 π + 12 πn

6 \cdot \frac{3 π}{2} + 6 \cdot 2 πn

6 \cdot \frac{3 π}{2} = 9 π

6 \cdot \frac{3 π}{2}

分式相乘:

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

= \frac{3 π 6}{2}

数字相乘:

3 \cdot 6 = 18

= \frac{18 π}{2}

数字相除:

\frac{18}{2} = 9

= 9 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= 9 π + 12 πn

π t = 9 π + 12 πn

π t = 9 π + 12 πn

π t = 9 π + 12 πn

两边除以

π

π t = 9 π + 12 πn

两边除以

π

\frac{π t}{π} = \frac{9 π}{π} + \frac{12 πn}{π}

化简

\frac{π t}{π} = \frac{9 π}{π} + \frac{12 πn}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{9 π}{π} + \frac{12 πn}{π} : 9 + 12 n

\frac{9 π}{π} + \frac{12 πn}{π}

消掉

\frac{9 π}{π} : 9

\frac{9 π}{π}

约分:

π

= 9

= 9 + \frac{12 πn}{π}

消掉

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

约分:

π

= 12 n

= 9 + 12 n

t = 9 + 12 n

t = 9 + 12 n

t = 9 + 12 n

t = 3 + 12 n, t = 9 + 12 n

作图

流行的例子

10cos^2(x)+9cos(x)+2=0

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sin (θ) = - 0.4

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