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受欢迎的三角函数 >

22=18+8cos((x+9)/(12)pi)

解答

22 = 18 + 8 cos (\frac{x + 9}{12} π)

解答

x = 24 n - 5, x = 24 n + 11

+1

度数

x = - 286.47889 \dots^{\circ} + 1375.09870 \dots^{\circ} n, x = 630.25357 \dots^{\circ} + 1375.09870 \dots^{\circ} n

求解步骤

22 = 18 + 8 cos (\frac{x + 9}{12} π)

交换两边

18 + 8 cos (\frac{x + 9}{12} π) = 22

将

18

到右边

18 + 8 cos (\frac{x + 9}{12} π) = 22

两边减去

18

18 + 8 cos (\frac{x + 9}{12} π) - 18 = 22 - 18

化简

8 cos (\frac{x + 9}{12} π) = 4

8 cos (\frac{x + 9}{12} π) = 4

两边除以

8

8 cos (\frac{x + 9}{12} π) = 4

两边除以

8

\frac{8 cos ( \frac{x + 9}{12} π )}{8} = \frac{4}{8}

化简

cos (\frac{x + 9}{12} π) = \frac{1}{2}

cos (\frac{x + 9}{12} π) = \frac{1}{2}

cos (\frac{x + 9}{12} π) = \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{x + 9}{12} π = \frac{π}{3} + 2 πn, \frac{x + 9}{12} π = \frac{5 π}{3} + 2 πn

\frac{x + 9}{12} π = \frac{π}{3} + 2 πn, \frac{x + 9}{12} π = \frac{5 π}{3} + 2 πn

解

\frac{x + 9}{12} π = \frac{π}{3} + 2 πn : x = 24 n - 5

\frac{x + 9}{12} π = \frac{π}{3} + 2 πn

分式相乘:

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

\frac{π ( x + 9 )}{12} = \frac{π}{3} + 2 πn

在两边乘以

12

\frac{π ( x + 9 )}{12} = \frac{π}{3} + 2 πn

在两边乘以

12

\frac{12 π ( x + 9 )}{12} = 12 \cdot \frac{π}{3} + 12 \cdot 2 πn

化简

\frac{12 π ( x + 9 )}{12} = 12 \cdot \frac{π}{3} + 12 \cdot 2 πn

化简

\frac{12 π ( x + 9 )}{12} : π (x + 9)

\frac{12 π ( x + 9 )}{12}

数字相除:

\frac{12}{12} = 1

= π (x + 9)

化简

12 \cdot \frac{π}{3} + 12 \cdot 2 πn : 4 π + 24 πn

12 \cdot \frac{π}{3} + 12 \cdot 2 πn

12 \cdot \frac{π}{3} = 4 π

12 \cdot \frac{π}{3}

分式相乘:

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

= \frac{π 12}{3}

数字相除:

\frac{12}{3} = 4

= 4 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 24 πn

= 4 π + 24 πn

π (x + 9) = 4 π + 24 πn

π (x + 9) = 4 π + 24 πn

π (x + 9) = 4 π + 24 πn

两边除以

π

π (x + 9) = 4 π + 24 πn

两边除以

π

\frac{π ( x + 9 )}{π} = \frac{4 π}{π} + \frac{24 πn}{π}

化简

\frac{π ( x + 9 )}{π} = \frac{4 π}{π} + \frac{24 πn}{π}

化简

\frac{π ( x + 9 )}{π} : x + 9

\frac{π ( x + 9 )}{π}

约分:

π

= x + 9

化简

\frac{4 π}{π} + \frac{24 πn}{π} : 4 + 24 n

\frac{4 π}{π} + \frac{24 πn}{π}

消掉

\frac{4 π}{π} : 4

\frac{4 π}{π}

约分:

π

= 4

= 4 + \frac{24 πn}{π}

消掉

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

约分:

π

= 24 n

= 4 + 24 n

x + 9 = 4 + 24 n

x + 9 = 4 + 24 n

x + 9 = 4 + 24 n

将

9

到右边

x + 9 = 4 + 24 n

两边减去

9

x + 9 - 9 = 4 + 24 n - 9

化简

x = 24 n - 5

x = 24 n - 5

解

\frac{x + 9}{12} π = \frac{5 π}{3} + 2 πn : x = 24 n + 11

\frac{x + 9}{12} π = \frac{5 π}{3} + 2 πn

分式相乘:

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

\frac{π ( x + 9 )}{12} = \frac{5 π}{3} + 2 πn

在两边乘以

12

\frac{π ( x + 9 )}{12} = \frac{5 π}{3} + 2 πn

在两边乘以

12

\frac{12 π ( x + 9 )}{12} = 12 \cdot \frac{5 π}{3} + 12 \cdot 2 πn

化简

\frac{12 π ( x + 9 )}{12} = 12 \cdot \frac{5 π}{3} + 12 \cdot 2 πn

化简

\frac{12 π ( x + 9 )}{12} : π (x + 9)

\frac{12 π ( x + 9 )}{12}

数字相除:

\frac{12}{12} = 1

= π (x + 9)

化简

12 \cdot \frac{5 π}{3} + 12 \cdot 2 πn : 20 π + 24 πn

12 \cdot \frac{5 π}{3} + 12 \cdot 2 πn

12 \cdot \frac{5 π}{3} = 20 π

12 \cdot \frac{5 π}{3}

分式相乘:

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

= \frac{5 π 12}{3}

数字相乘:

5 \cdot 12 = 60

= \frac{60 π}{3}

数字相除:

\frac{60}{3} = 20

= 20 π

12 \cdot 2 πn = 24 πn

12 \cdot 2 πn

数字相乘:

12 \cdot 2 = 24

= 24 πn

= 20 π + 24 πn

π (x + 9) = 20 π + 24 πn

π (x + 9) = 20 π + 24 πn

π (x + 9) = 20 π + 24 πn

两边除以

π

π (x + 9) = 20 π + 24 πn

两边除以

π

\frac{π ( x + 9 )}{π} = \frac{20 π}{π} + \frac{24 πn}{π}

化简

\frac{π ( x + 9 )}{π} = \frac{20 π}{π} + \frac{24 πn}{π}

化简

\frac{π ( x + 9 )}{π} : x + 9

\frac{π ( x + 9 )}{π}

约分:

π

= x + 9

化简

\frac{20 π}{π} + \frac{24 πn}{π} : 20 + 24 n

\frac{20 π}{π} + \frac{24 πn}{π}

消掉

\frac{20 π}{π} : 20

\frac{20 π}{π}

约分:

π

= 20

= 20 + \frac{24 πn}{π}

消掉

\frac{24 πn}{π} : 24 n

\frac{24 πn}{π}

约分:

π

= 24 n

= 20 + 24 n

x + 9 = 20 + 24 n

x + 9 = 20 + 24 n

x + 9 = 20 + 24 n

将

9

到右边

x + 9 = 20 + 24 n

两边减去

9

x + 9 - 9 = 20 + 24 n - 9

化简

x = 24 n + 11

x = 24 n + 11

x = 24 n - 5, x = 24 n + 11

作图

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