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^2(x)=-7sin(x)-4,0<= x<= 2pi

解答

3 sin^{2} (x) = - 7 sin (x) - 4, 0 \leq x \leq 2 π

解答

x = \frac{3 π}{2}

+1

度数

x = 27 0^{\circ}

求解步骤

3 sin^{2} (x) = - 7 sin (x) - 4, 0 \leq x \leq 2 π

用替代法求解

3 sin^{2} (x) = - 7 sin (x) - 4

令

: sin (x) = u

3 u^{2} = - 7 u - 4

3 u^{2} = - 7 u - 4 : u = - 1, u = - \frac{4}{3}

3 u^{2} = - 7 u - 4

将

4

para o lado esquerdo

3 u^{2} = - 7 u - 4

两边加上

4

3 u^{2} + 4 = - 7 u - 4 + 4

化简

3 u^{2} + 4 = - 7 u

3 u^{2} + 4 = - 7 u

将

7 u

para o lado esquerdo

3 u^{2} + 4 = - 7 u

两边加上

7 u

3 u^{2} + 4 + 7 u = - 7 u + 7 u

化简

3 u^{2} + 4 + 7 u = 0

3 u^{2} + 4 + 7 u = 0

改写成标准形式

a x^{2} + b x + c = 0

3 u^{2} + 7 u + 4 = 0

使用求根公式求解

3 u^{2} + 7 u + 4 = 0

二次方程求根公式:

若

a = 3, b = 7, c = 4

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

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

7^{2} - 4 \cdot 3 \cdot 4 = 1

7^{2} - 4 \cdot 3 \cdot 4

数字相乘:

4 \cdot 3 \cdot 4 = 48

= 7^{2} - 48

7^{2} = 49

= 49 - 48

数字相减:

49 - 48 = 1

= 1

使用法则

1 = 1

= 1

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

将解分隔开

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

u = \frac{- 7 + 1}{2 \cdot 3} : - 1

\frac{- 7 + 1}{2 \cdot 3}

数字相加/相减:

- 7 + 1 = - 6

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

数字相乘:

2 \cdot 3 = 6

= \frac{- 6}{6}

使用分式法则:

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

= - \frac{6}{6}

使用法则

\frac{a}{a} = 1

= - 1

u = \frac{- 7 - 1}{2 \cdot 3} : - \frac{4}{3}

\frac{- 7 - 1}{2 \cdot 3}

数字相减:

- 7 - 1 = - 8

= \frac{- 8}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 8}{6}

使用分式法则:

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

= - \frac{8}{6}

约分:

2

= - \frac{4}{3}

二次方程组的解是:

u = - 1, u = - \frac{4}{3}

u = sin (x)

代回

sin (x) = - 1, sin (x) = - \frac{4}{3}

sin (x) = - 1, sin (x) = - \frac{4}{3}

sin (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

sin (x) = - 1, 0 \leq x \leq 2 π

sin (x) = - 1

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 = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{3 π}{2}

sin (x) = - \frac{4}{3}, 0 \leq x \leq 2 π :

无解

sin (x) = - \frac{4}{3}, 0 \leq x \leq 2 π

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = \frac{3 π}{2}

作图

流行的例子

sin(-θ)=sin(θ)

sin (- θ) = sin (θ)

4cos^2(x)+4cos(x)=3

4 cos^{2} (x) + 4 cos (x) = 3

sec(2x)csc(2x)=2csc(2x)

sec (2 x) csc (2 x) = 2 csc (2 x)

3cos(x)tan(x)=-10tan(x)

3 cos (x) tan (x) = - 10 tan (x)

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

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