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受欢迎的三角函数 >

sin(2x)=sin(x)cos(x)

解答

sin (2 x) = sin (x) cos (x)

解答

x = πn, x = \frac{π}{2} + πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x) = sin (x) cos (x)

两边减去

sin (x) cos (x)

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

使用三角恒等式改写

sin (2 x) - cos (x) sin (x)

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

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

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

化简

sin (2 x) - \frac{sin ( 2 x )}{2} : \frac{sin ( 2 x )}{2}

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

将项转换为分式:

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

= - \frac{sin ( 2 x )}{2} + \frac{sin ( 2 x ) \cdot 2}{2}

因为分母相等，所以合并分式:

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

= \frac{- sin ( 2 x ) + sin ( 2 x ) \cdot 2}{2}

同类项相加:

- sin (2 x) + 2 sin (2 x) = sin (2 x)

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

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

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

在两边乘以

2

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

在两边乘以

2

\frac{2 sin ( 2 x )}{2} = 0 \cdot 2

化简

sin (2 x) = 0

sin (2 x) = 0

sin (2 x) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

解

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

两边除以

2

2 x = 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 πn}{2}

化简

x = πn

x = πn

解

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

两边除以

2

2 x = π + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

作图

流行的例子

sin(θ)=-(sqrt(5))/5 ,(3pi)/2 <θ<2pi

sin (θ) = - \frac{5}{5}, \frac{3 π}{2} < θ < 2 π

(2sin(2x)-1)(3tan(2x)-1)=0

(2 sin (2 x) - 1) (3 tan (2 x) - 1) = 0

-0.2588+0.9659tan(b)=1.4201

- 0.2588 + 0.9659 tan (b) = 1.4201

2cot^2(t)sin(t)-cot^2(t)=0

2 cot^{2} (t) sin (t) - cot^{2} (t) = 0

7 cos (x) = - 1