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受欢迎的三角函数 >

sin(2x)=-5cos(2x)

解答

sin (2 x) = - 5 cos (2 x)

解答

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

+1

度数

x = - 39.34503 \dots^{\circ} + 9 0^{\circ} n

求解步骤

sin (2 x) = - 5 cos (2 x)

使用三角恒等式改写

sin (2 x) = - 5 cos (2 x)

在两边除以

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

\frac{sin ( 2 x )}{cos ( 2 x )} = \frac{- 5 cos ( 2 x )}{cos ( 2 x )}

化简

\frac{sin ( 2 x )}{cos ( 2 x )} = - 5

使用基本三角恒等式:

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

tan (2 x) = - 5

tan (2 x) = - 5

使用反三角函数性质

tan (2 x) = - 5

tan (2 x) = - 5

的通解

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

2 x = arctan (- 5) + πn

2 x = arctan (- 5) + πn

解

2 x = arctan (- 5) + πn : x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

2 x = arctan (- 5) + πn

化简

arctan (- 5) + πn : - arctan (5) + πn

arctan (- 5) + πn

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= - arctan (5) + πn

2 x = - arctan (5) + πn

两边除以

2

2 x = - arctan (5) + πn

两边除以

2

\frac{2 x}{2} = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

化简

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

以小数形式表示解

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

作图

流行的例子

tan(x)cot(x)=sec(x)csc(x)

tan (x) cot (x) = sec (x) csc (x)

4sin(x)=cos(x)-2

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

sin(θ)=1-cos(θ)

sin (θ) = 1 - cos (θ)

cos(θ)-2sin(θ)cos(θ)=0

cos (θ) - 2 sin (θ) cos (θ) = 0

solvefor x,cos(xy)=sin(x+y)

so l v e f or x, cos (x y) = sin (x + y)