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 >

2sin^2(x)+sin(x)+1=0

解答

2 sin^{2} (x) + sin (x) + 1 = 0

解答

x \in R 无解

求解步骤

2 sin^{2} (x) + sin (x) + 1 = 0

用替代法求解

2 sin^{2} (x) + sin (x) + 1 = 0

令

: sin (x) = u

2 u^{2} + u + 1 = 0

2 u^{2} + u + 1 = 0 : u = - \frac{1}{4} + i \frac{7}{4}, u = - \frac{1}{4} - i \frac{7}{4}

2 u^{2} + u + 1 = 0

使用求根公式求解

2 u^{2} + u + 1 = 0

二次方程求根公式:

若

a = 2, b = 1, c = 1

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

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

化简

1^{2} - 4 \cdot 2 \cdot 1 : 7 i

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

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 2 \cdot 1

数字相乘:

4 \cdot 2 \cdot 1 = 8

= 1 - 8

数字相减:

1 - 8 = - 7

= - 7

使用根式运算法则:

- a = - 1 a

- 7 = - 1 7

= - 1 7

使用虚数运算法则:

- 1 = i

= 7 i

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

将解分隔开

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

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 1 + 7 i}{4}

将

\frac{- 1 + 7 i}{4}

改写成标准复数形式:

- \frac{1}{4} + \frac{7}{4} i

\frac{- 1 + 7 i}{4}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 1 + 7 i}{4} = - \frac{1}{4} + \frac{7 i}{4}

= - \frac{1}{4} + \frac{7 i}{4}

= - \frac{1}{4} + \frac{7}{4} i

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 1 - 7 i}{4}

将

\frac{- 1 - 7 i}{4}

改写成标准复数形式:

- \frac{1}{4} - \frac{7}{4} i

\frac{- 1 - 7 i}{4}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 1 - 7 i}{4} = - \frac{1}{4} - \frac{7 i}{4}

= - \frac{1}{4} - \frac{7 i}{4}

= - \frac{1}{4} - \frac{7}{4} i

二次方程组的解是:

u = - \frac{1}{4} + i \frac{7}{4}, u = - \frac{1}{4} - i \frac{7}{4}

u = sin (x)

代回

sin (x) = - \frac{1}{4} + i \frac{7}{4}, sin (x) = - \frac{1}{4} - i \frac{7}{4}

sin (x) = - \frac{1}{4} + i \frac{7}{4}, sin (x) = - \frac{1}{4} - i \frac{7}{4}

sin (x) = - \frac{1}{4} + i \frac{7}{4} :

无解

sin (x) = - \frac{1}{4} + i \frac{7}{4}

无解

sin (x) = - \frac{1}{4} - i \frac{7}{4} :

无解

sin (x) = - \frac{1}{4} - i \frac{7}{4}

无解

合并所有解

x \in R 无解

作图

流行的例子

sin (x) = \frac{20}{29}

7 cos^{2} (x) - 2 = 0

tan(θ/2+pi/6)=-1

tan (\frac{θ}{2} + \frac{π}{6}) = - 1

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

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

cos (x) = - 0.3