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受欢迎的三角函数 >

3sin^2(x)-6sin(x)=0

解答

3 sin^{2} (x) - 6 sin (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^{2} (x) - 6 sin (x) = 0

用替代法求解

3 sin^{2} (x) - 6 sin (x) = 0

令

: sin (x) = u

3 u^{2} - 6 u = 0

3 u^{2} - 6 u = 0 : u = 2, u = 0

3 u^{2} - 6 u = 0

使用求根公式求解

3 u^{2} - 6 u = 0

二次方程求根公式:

若

a = 3, b = - 6, c = 0

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 \cdot 0 = 6

(- 6)^{2} - 4 \cdot 3 \cdot 0

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 6)^{2} = 6^{2}

= 6^{2} - 4 \cdot 3 \cdot 0

使用法则

0 \cdot a = 0

= 6^{2} - 0

6^{2} - 0 = 6^{2}

= 6^{2}

使用根式运算法则:

假定

a \geq 0

= 6

u_{1, 2} = \frac{- ( - 6 ) \pm 6}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- ( - 6 ) + 6}{2 \cdot 3}, u_{2} = \frac{- ( - 6 ) - 6}{2 \cdot 3}

u = \frac{- ( - 6 ) + 6}{2 \cdot 3} : 2

\frac{- ( - 6 ) + 6}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{6 + 6}{2 \cdot 3}

数字相加:

6 + 6 = 12

= \frac{12}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{12}{6}

数字相除:

\frac{12}{6} = 2

= 2

u = \frac{- ( - 6 ) - 6}{2 \cdot 3} : 0

\frac{- ( - 6 ) - 6}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{6 - 6}{2 \cdot 3}

数字相减:

6 - 6 = 0

= \frac{0}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{0}{6}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

二次方程组的解是:

u = 2, u = 0

u = sin (x)

代回

sin (x) = 2, sin (x) = 0

sin (x) = 2, sin (x) = 0

sin (x) = 2 :

无解

sin (x) = 2

- 1 \leq sin (x) \leq 1

无解

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

合并所有解

x = 2 πn, x = π + 2 πn

作图

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15cos((2pi)/(365)t)+43=30