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 >

sin^2(x)+8sin(x)-9=0

解答

sin^{2} (x) + 8 sin (x) - 9 = 0

解答

x = \frac{π}{2} + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) + 8 sin (x) - 9 = 0

用替代法求解

sin^{2} (x) + 8 sin (x) - 9 = 0

令

: sin (x) = u

u^{2} + 8 u - 9 = 0

u^{2} + 8 u - 9 = 0 : u = 1, u = - 9

u^{2} + 8 u - 9 = 0

使用求根公式求解

u^{2} + 8 u - 9 = 0

二次方程求根公式:

若

a = 1, b = 8, c = - 9

u_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 1 \cdot ( - 9 )}{2 \cdot 1}

u_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 1 \cdot ( - 9 )}{2 \cdot 1}

8^{2} - 4 \cdot 1 \cdot (- 9) = 10

8^{2} - 4 \cdot 1 \cdot (- 9)

使用法则

- (- a) = a

= 8^{2} + 4 \cdot 1 \cdot 9

数字相乘:

4 \cdot 1 \cdot 9 = 36

= 8^{2} + 36

8^{2} = 64

= 64 + 36

数字相加:

64 + 36 = 100

= 100

因式分解数字:

100 = 1 0^{2}

= 1 0^{2}

使用根式运算法则:

n a^{n} = a

1 0^{2} = 10

= 10

u_{1, 2} = \frac{- 8 \pm 10}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- 8 + 10}{2 \cdot 1}, u_{2} = \frac{- 8 - 10}{2 \cdot 1}

u = \frac{- 8 + 10}{2 \cdot 1} : 1

\frac{- 8 + 10}{2 \cdot 1}

数字相加/相减:

- 8 + 10 = 2

= \frac{2}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{2}{2}

使用法则

\frac{a}{a} = 1

= 1

u = \frac{- 8 - 10}{2 \cdot 1} : - 9

\frac{- 8 - 10}{2 \cdot 1}

数字相减:

- 8 - 10 = - 18

= \frac{- 18}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 18}{2}

使用分式法则:

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

= - \frac{18}{2}

数字相除:

\frac{18}{2} = 9

= - 9

二次方程组的解是:

u = 1, u = - 9

u = sin (x)

代回

sin (x) = 1, sin (x) = - 9

sin (x) = 1, sin (x) = - 9

sin (x) = 1 : x = \frac{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{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

sin (x) = - 9 :

无解

sin (x) = - 9

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = \frac{π}{2} + 2 πn

作图

流行的例子

-2sin^2(θ)+10sin(θ)-3=3sin(θ),0<= θ<360

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ), 0^{\circ} \leq θ < 36 0^{\circ}

cot^2(θ)+4csc(θ)=-5

cot^{2} (θ) + 4 csc (θ) = - 5

10sin(a)+7sin(a)+1sin(a)+8sin(a)=48

10 sin (a) + 7 sin (a) + 1 sin (a) + 8 sin (a) = 48

2cos^2(θ)+7sin(θ)=5

2 cos^{2} (θ) + 7 sin (θ) = 5

(2sqrt(3))/3 =sec(θ)

\frac{2 3}{3} = sec (θ)