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受欢迎的三角函数 >

3sin^2(x)-7sin(x)=6

解答

3 sin^{2} (x) - 7 sin (x) = 6

解答

x = - 0.72972 \dots + 2 πn, x = π + 0.72972 \dots + 2 πn

+1

度数

x = - 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 221.81031 \dots^{\circ} + 36 0^{\circ} n

求解步骤

3 sin^{2} (x) - 7 sin (x) = 6

用替代法求解

3 sin^{2} (x) - 7 sin (x) = 6

令

: sin (x) = u

3 u^{2} - 7 u = 6

3 u^{2} - 7 u = 6 : u = 3, u = - \frac{2}{3}

3 u^{2} - 7 u = 6

将

6

para o lado esquerdo

3 u^{2} - 7 u = 6

两边减去

6

3 u^{2} - 7 u - 6 = 6 - 6

化简

3 u^{2} - 7 u - 6 = 0

3 u^{2} - 7 u - 6 = 0

使用求根公式求解

3 u^{2} - 7 u - 6 = 0

二次方程求根公式:

若

a = 3, b = - 7, c = - 6

u_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 3 ( - 6 )}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 3 ( - 6 )}{2 \cdot 3}

(- 7)^{2} - 4 \cdot 3 (- 6) = 11

(- 7)^{2} - 4 \cdot 3 (- 6)

使用法则

- (- a) = a

= (- 7)^{2} + 4 \cdot 3 \cdot 6

使用指数法则:

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

若

n

是偶数

(- 7)^{2} = 7^{2}

= 7^{2} + 4 \cdot 3 \cdot 6

数字相乘:

4 \cdot 3 \cdot 6 = 72

= 7^{2} + 72

7^{2} = 49

= 49 + 72

数字相加:

49 + 72 = 121

= 121

因式分解数字:

121 = 1 1^{2}

= 1 1^{2}

使用根式运算法则:

n a^{n} = a

1 1^{2} = 11

= 11

u_{1, 2} = \frac{- ( - 7 ) \pm 11}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- ( - 7 ) + 11}{2 \cdot 3}, u_{2} = \frac{- ( - 7 ) - 11}{2 \cdot 3}

u = \frac{- ( - 7 ) + 11}{2 \cdot 3} : 3

\frac{- ( - 7 ) + 11}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{7 + 11}{2 \cdot 3}

数字相加:

7 + 11 = 18

= \frac{18}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{18}{6}

数字相除:

\frac{18}{6} = 3

= 3

u = \frac{- ( - 7 ) - 11}{2 \cdot 3} : - \frac{2}{3}

\frac{- ( - 7 ) - 11}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{7 - 11}{2 \cdot 3}

数字相减:

7 - 11 = - 4

= \frac{- 4}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 4}{6}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{6}

约分:

2

= - \frac{2}{3}

二次方程组的解是:

u = 3, u = - \frac{2}{3}

u = sin (x)

代回

sin (x) = 3, sin (x) = - \frac{2}{3}

sin (x) = 3, sin (x) = - \frac{2}{3}

sin (x) = 3 :

无解

sin (x) = 3

- 1 \leq sin (x) \leq 1

无解

sin (x) = - \frac{2}{3} : x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

sin (x) = - \frac{2}{3}

使用反三角函数性质

sin (x) = - \frac{2}{3}

sin (x) = - \frac{2}{3}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

合并所有解

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

以小数形式表示解

x = - 0.72972 \dots + 2 πn, x = π + 0.72972 \dots + 2 πn

作图

流行的例子

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