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受欢迎的三角函数 >

tan(2x)=-0.5

解答

tan (2 x) = - 0.5

解答

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

+1

度数

x = - 13.28252 \dots^{\circ} + 9 0^{\circ} n

求解步骤

tan (2 x) = - 0.5

使用反三角函数性质

tan (2 x) = - 0.5

tan (2 x) = - 0.5

的通解

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

2 x = arctan (- 0.5) + πn

2 x = arctan (- 0.5) + πn

解

2 x = arctan (- 0.5) + πn : x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

2 x = arctan (- 0.5) + πn

化简

arctan (- 0.5) + πn : - arctan (\frac{1}{2}) + πn

arctan (- 0.5) + πn

arctan (- 0.5) = - arctan (\frac{1}{2})

arctan (- 0.5)

= arctan (- \frac{1}{2})

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{2}) = - arctan (\frac{1}{2})

= - arctan (\frac{1}{2})

= - arctan (\frac{1}{2}) + πn

2 x = - arctan (\frac{1}{2}) + πn

两边除以

2

2 x = - arctan (\frac{1}{2}) + πn

两边除以

2

\frac{2 x}{2} = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

化简

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

以小数形式表示解

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

作图

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