zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

3sin(x)-2sin(x)cos(x)=0

解答

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

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

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

分解

3 sin (x) - 2 sin (x) cos (x) : - sin (x) (2 cos (x) - 3)

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

因式分解出通项

- sin (x)

= - sin (x) (- 3 + 2 cos (x))

- sin (x) (2 cos (x) - 3) = 0

分别求解每个部分

sin (x) = 0 or 2 cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

2 cos (x) - 3 = 0 :

无解

2 cos (x) - 3 = 0

将

3

到右边

2 cos (x) - 3 = 0

两边加上

3

2 cos (x) - 3 + 3 = 0 + 3

化简

2 cos (x) = 3

2 cos (x) = 3

两边除以

2

2 cos (x) = 3

两边除以

2

\frac{2 cos ( x )}{2} = \frac{3}{2}

化简

cos (x) = \frac{3}{2}

cos (x) = \frac{3}{2}

- 1 \leq cos (x) \leq 1

无解

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

8tan(b)+12=3tan(b)+7

8 tan (b) + 12 = 3 tan (b) + 7

sin(θ)+sqrt(2)=-sin(θ)

sin (θ) + 2 = - sin (θ)

cos (x) = π

3 cot (θ) + 1 = 0

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

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