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受欢迎的三角函数 >

tan(4x+6)=-0.272

解答

tan (4 x + 6) = - 0.272

解答

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

+1

度数

x = - 89.74775 \dots^{\circ} + 4 5^{\circ} n

求解步骤

tan (4 x + 6) = - 0.272

使用反三角函数性质

tan (4 x + 6) = - 0.272

tan (4 x + 6) = - 0.272

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

4 x + 6 = arctan (- 0.272) + πn

4 x + 6 = arctan (- 0.272) + πn

解

4 x + 6 = arctan (- 0.272) + πn : x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

4 x + 6 = arctan (- 0.272) + πn

化简

arctan (- 0.272) + πn : - arctan (\frac{34}{125}) + πn

arctan (- 0.272) + πn

arctan (- 0.272) = - arctan (\frac{34}{125})

arctan (- 0.272)

= arctan (- \frac{34}{125})

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- \frac{34}{125}) = - arctan (\frac{34}{125})

= - arctan (\frac{34}{125})

= - arctan (\frac{34}{125}) + πn

4 x + 6 = - arctan (\frac{34}{125}) + πn

将

6

到右边

4 x + 6 = - arctan (\frac{34}{125}) + πn

两边减去

6

4 x + 6 - 6 = - arctan (\frac{34}{125}) + πn - 6

化简

4 x = - arctan (\frac{34}{125}) + πn - 6

4 x = - arctan (\frac{34}{125}) + πn - 6

两边除以

4

4 x = - arctan (\frac{34}{125}) + πn - 6

两边除以

4

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

化简

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4} : - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

对同类项分组

= - \frac{6}{4} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

消掉

\frac{6}{4} : \frac{3}{2}

\frac{6}{4}

约分:

2

= \frac{3}{2}

= - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

以小数形式表示解

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

作图

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