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受欢迎的三角函数 >

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

解答

sin (2 x) - 2 cos (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

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

使用三角恒等式改写

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

在两边除以

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

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

化简

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

使用基本三角恒等式:

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

tan (2 x) - 2 = 0

tan (2 x) - 2 = 0

将

2

到右边

tan (2 x) - 2 = 0

两边加上

2

tan (2 x) - 2 + 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

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

tan(x)=(87.092)/(86.676)

tan (x) = \frac{87.092}{86.676}

csc (x) = - \frac{3}{2}

1 + 3 sin (θ) = 0

(tan(2x))/(sin(x))=-2

\frac{tan ( 2 x )}{sin ( x )} = - 2

sin (A) = 0.5