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受欢迎的三角函数 >

2cos(2x)+sin(2x)=0

解答

2 cos (2 x) + sin (2 x) = 0

解答

x = - \frac{1.10714 \dots}{2} + \frac{πn}{2}

+1

度数

x = - 31.71747 \dots^{\circ} + 9 0^{\circ} n

求解步骤

2 cos (2 x) + sin (2 x) = 0

使用三角恒等式改写

2 cos (2 x) + sin (2 x) = 0

在两边除以

cos (2 x), cos (2 x) \neq = 0

\frac{2 cos ( 2 x ) + sin ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

化简

2 + \frac{sin ( 2 x )}{cos ( 2 x )} = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 + tan (2 x) = 0

2 + tan (2 x) = 0

将

2

到右边

2 + tan (2 x) = 0

两边减去

2

2 + tan (2 x) - 2 = 0 - 2

化简

tan (2 x) = - 2

tan (2 x) = - 2

使用反三角函数性质

tan (2 x) = - 2

tan (2 x) = - 2

的通解

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

2 x = arctan (- 2) + πn

2 x = arctan (- 2) + πn

解

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

2 x = arctan (- 2) + πn

化简

arctan (- 2) + πn : - arctan (2) + πn

arctan (- 2) + πn

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 2) = - arctan (2)

= - arctan (2) + πn

2 x = - arctan (2) + πn

两边除以

2

2 x = - arctan (2) + πn

两边除以

2

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

化简

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

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

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

以小数形式表示解

x = - \frac{1.10714 \dots}{2} + \frac{πn}{2}

作图

流行的例子

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csc^{2} (θ) - cot (θ) = 1

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sin (x) = \frac{2}{13}

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