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受欢迎的三角函数 >

2tan(2x)-10=3.4641

解答

2 tan (2 x) - 10 = 3.4641

解答

x = \frac{1.42333 \dots}{2} + \frac{πn}{2}

+1

度数

x = 40.77544 \dots^{\circ} + 9 0^{\circ} n

求解步骤

2 tan (2 x) - 10 = 3.4641

将

10

到右边

2 tan (2 x) - 10 = 3.4641

两边加上

10

2 tan (2 x) - 10 + 10 = 3.4641 + 10

化简

2 tan (2 x) = 13.4641

2 tan (2 x) = 13.4641

两边除以

2

2 tan (2 x) = 13.4641

两边除以

2

\frac{2 tan ( 2 x )}{2} = \frac{13.4641}{2}

化简

tan (2 x) = \frac{13.4641}{2}

tan (2 x) = \frac{13.4641}{2}

使用反三角函数性质

tan (2 x) = \frac{13.4641}{2}

tan (2 x) = \frac{13.4641}{2}

的通解

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

2 x = arctan (\frac{13.4641}{2}) + πn

2 x = arctan (\frac{13.4641}{2}) + πn

解

2 x = arctan (\frac{13.4641}{2}) + πn : x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{13.4641}{2}) + πn

两边除以

2

2 x = arctan (\frac{13.4641}{2}) + πn

两边除以

2

\frac{2 x}{2} = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

化简

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

以小数形式表示解

x = \frac{1.42333 \dots}{2} + \frac{πn}{2}

作图

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