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受欢迎的三角函数 >

tan(x/2-pi/2)=sqrt(2)

解答

tan (\frac{x}{2} - \frac{π}{2}) = 2

解答

x = 2 \cdot 0.95531 \dots + 2 πn + π

+1

度数

x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

求解步骤

tan (\frac{x}{2} - \frac{π}{2}) = 2

使用反三角函数性质

tan (\frac{x}{2} - \frac{π}{2}) = 2

tan (\frac{x}{2} - \frac{π}{2}) = 2

的通解

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

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

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

解

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

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

将

\frac{π}{2}

到右边

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

两边加上

\frac{π}{2}

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

化简

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

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

在两边乘以

2

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

在两边乘以

2

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

化简

\frac{2 x}{2} = 2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2} : 2 arctan (2) + 2 πn + π

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

分式相乘:

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

= \frac{π 2}{2}

约分:

2

= π

= 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

以小数形式表示解

x = 2 \cdot 0.95531 \dots + 2 πn + π

作图

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