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 >

8sin^2(x)+12sin(x)+4=0

解答

8 sin^{2} (x) + 12 sin (x) + 4 = 0

解答

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

度数

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

8 sin^{2} (x) + 12 sin (x) + 4 = 0

用替代法求解

8 sin^{2} (x) + 12 sin (x) + 4 = 0

令

: sin (x) = u

8 u^{2} + 12 u + 4 = 0

8 u^{2} + 12 u + 4 = 0 : u = - \frac{1}{2}, u = - 1

8 u^{2} + 12 u + 4 = 0

使用求根公式求解

8 u^{2} + 12 u + 4 = 0

二次方程求根公式:

若

a = 8, b = 12, c = 4

u_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 8 \cdot 4}{2 \cdot 8}

u_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 8 \cdot 4}{2 \cdot 8}

1 2^{2} - 4 \cdot 8 \cdot 4 = 4

1 2^{2} - 4 \cdot 8 \cdot 4

数字相乘:

4 \cdot 8 \cdot 4 = 128

= 1 2^{2} - 128

1 2^{2} = 144

= 144 - 128

数字相减:

144 - 128 = 16

= 16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

u_{1, 2} = \frac{- 12 \pm 4}{2 \cdot 8}

将解分隔开

u_{1} = \frac{- 12 + 4}{2 \cdot 8}, u_{2} = \frac{- 12 - 4}{2 \cdot 8}

u = \frac{- 12 + 4}{2 \cdot 8} : - \frac{1}{2}

\frac{- 12 + 4}{2 \cdot 8}

数字相加/相减:

- 12 + 4 = - 8

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

数字相乘:

2 \cdot 8 = 16

= \frac{- 8}{16}

使用分式法则:

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

= - \frac{8}{16}

约分:

8

= - \frac{1}{2}

u = \frac{- 12 - 4}{2 \cdot 8} : - 1

\frac{- 12 - 4}{2 \cdot 8}

数字相减:

- 12 - 4 = - 16

= \frac{- 16}{2 \cdot 8}

数字相乘:

2 \cdot 8 = 16

= \frac{- 16}{16}

使用分式法则:

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

= - \frac{16}{16}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = - \frac{1}{2}, u = - 1

u = sin (x)

代回

sin (x) = - \frac{1}{2}, sin (x) = - 1

sin (x) = - \frac{1}{2}, sin (x) = - 1

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2}

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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = - 1

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

合并所有解

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

作图

流行的例子

4sin^2(x)=cos(x)+1

4 sin^{2} (x) = cos (x) + 1

0 = 4 sin (x)

sec^2(θ)(1+cos^2(θ))=2-tan^2(θ)

sec^{2} (θ) (1 + cos^{2} (θ)) = 2 - tan^{2} (θ)

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

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

2sin(3x)cos(3x)=1

2 sin (3 x) cos (3 x) = 1