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(w)+sin(w)-1=0

解答

2 sin^{2} (w) + sin (w) - 1 = 0

解答

w = \frac{π}{6} + 2 πn, w = \frac{5 π}{6} + 2 πn, w = \frac{3 π}{2} + 2 πn

+1

度数

w = 3 0^{\circ} + 36 0^{\circ} n, w = 15 0^{\circ} + 36 0^{\circ} n, w = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin^{2} (w) + sin (w) - 1 = 0

用替代法求解

2 sin^{2} (w) + sin (w) - 1 = 0

令

: sin (w) = u

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

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

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 ( - 1 )}{2 \cdot 2}

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

1^{2} - 4 \cdot 2 (- 1) = 3

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

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 2 (- 1)

使用法则

- (- a) = a

= 1 + 4 \cdot 2 \cdot 1

数字相乘:

4 \cdot 2 \cdot 1 = 8

= 1 + 8

数字相加:

1 + 8 = 9

= 9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

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

将解分隔开

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

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

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

数字相加/相减:

- 1 + 3 = 2

= \frac{2}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

约分:

2

= \frac{1}{2}

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

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

数字相减:

- 1 - 3 = - 4

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 4}{4}

使用分式法则:

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

= - \frac{4}{4}

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 (w)

代回

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

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

sin (w) = \frac{1}{2} : w = \frac{π}{6} + 2 πn, w = \frac{5 π}{6} + 2 πn

sin (w) = \frac{1}{2}

sin (w) = \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}

w = \frac{π}{6} + 2 πn, w = \frac{5 π}{6} + 2 πn

w = \frac{π}{6} + 2 πn, w = \frac{5 π}{6} + 2 πn

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

sin (w) = - 1

sin (w) = - 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}

w = \frac{3 π}{2} + 2 πn

w = \frac{3 π}{2} + 2 πn

合并所有解

w = \frac{π}{6} + 2 πn, w = \frac{5 π}{6} + 2 πn, w = \frac{3 π}{2} + 2 πn

作图

流行的例子

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

sin^{2} (x) + sin (x) = - cos^{2} (x)

arctan(x)=arccos(3/4)

arctan (x) = arccos (\frac{3}{4})

tan^2(θ)+7tan(θ)+9=0

tan^{2} (θ) + 7 tan (θ) + 9 = 0

solvefor x,cos(x)*cos(y)=0

so l v e f or x, cos (x) \cdot cos (y) = 0

3 sec (θ) = 6