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受欢迎的三角函数 >

3tan(x)sin(x)-sqrt(3)sin(x)=0

解答

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

解答

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 18 0^{\circ} n

求解步骤

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

分解

3 tan (x) sin (x) - 3 sin (x) : sin (x) (3 tan (x) - 3)

3 tan (x) sin (x) - 3 sin (x)

因式分解出通项

sin (x)

= sin (x) (3 tan (x) - 3)

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

分别求解每个部分

sin (x) = 0 or 3 tan (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

3 tan (x) - 3 = 0 : x = \frac{π}{6} + πn

3 tan (x) - 3 = 0

将

3

到右边

3 tan (x) - 3 = 0

两边加上

3

3 tan (x) - 3 + 3 = 0 + 3

化简

3 tan (x) = 3

3 tan (x) = 3

两边除以

3

3 tan (x) = 3

两边除以

3

\frac{3 tan ( x )}{3} = \frac{3}{3}

化简

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

合并所有解

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + πn

作图

流行的例子

cot^4(x)-3cot^2(x)+1=0

cot^{4} (x) - 3 cot^{2} (x) + 1 = 0

(cos(-30+x))/(cos(30+x))= 1835/726

\frac{cos ( - 3 0 ^{\circ} + x )}{cos ( 3 0 ^{\circ} + x )} = \frac{1835}{726}

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

sin^{2} (x) = 3 cos (x) - 2

4sin(2x+pi/6)=2

4 sin (2 x + \frac{π}{6}) = 2

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