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 >

csc^2(x)+3csc(x)-4=0

解答

csc^{2} (x) + 3 csc (x) - 4 = 0

解答

x = \frac{π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 194.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

csc^{2} (x) + 3 csc (x) - 4 = 0

用替代法求解

csc^{2} (x) + 3 csc (x) - 4 = 0

令

: csc (x) = u

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

u^{2} + 3 u - 4 = 0 : u = 1, u = - 4

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

使用求根公式求解

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

二次方程求根公式:

若

a = 1, b = 3, c = - 4

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

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

3^{2} - 4 \cdot 1 \cdot (- 4) = 5

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

使用法则

- (- a) = a

= 3^{2} + 4 \cdot 1 \cdot 4

数字相乘:

4 \cdot 1 \cdot 4 = 16

= 3^{2} + 16

3^{2} = 9

= 9 + 16

数字相加:

9 + 16 = 25

= 25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

u_{1, 2} = \frac{- 3 \pm 5}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- 3 + 5}{2 \cdot 1}, u_{2} = \frac{- 3 - 5}{2 \cdot 1}

u = \frac{- 3 + 5}{2 \cdot 1} : 1

\frac{- 3 + 5}{2 \cdot 1}

数字相加/相减:

- 3 + 5 = 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{- 3 - 5}{2 \cdot 1} : - 4

\frac{- 3 - 5}{2 \cdot 1}

数字相减:

- 3 - 5 = - 8

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 8}{2}

使用分式法则:

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

= - \frac{8}{2}

数字相除:

\frac{8}{2} = 4

= - 4

二次方程组的解是:

u = 1, u = - 4

u = csc (x)

代回

csc (x) = 1, csc (x) = - 4

csc (x) = 1, csc (x) = - 4

csc (x) = 1 : x = \frac{π}{2} + 2 πn

csc (x) = 1

csc (x) = 1

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

csc (x) = - 4 : x = arccsc (- 4) + 2 πn, x = π + arccsc (4) + 2 πn

csc (x) = - 4

使用反三角函数性质

csc (x) = - 4

csc (x) = - 4

的通解

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

x = arccsc (- 4) + 2 πn, x = π + arccsc (4) + 2 πn

x = arccsc (- 4) + 2 πn, x = π + arccsc (4) + 2 πn

合并所有解

x = \frac{π}{2} + 2 πn, x = arccsc (- 4) + 2 πn, x = π + arccsc (4) + 2 πn

以小数形式表示解

x = \frac{π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

作图

流行的例子

cos^2(φ)=sin^2(φ)

cos^{2} (φ) = sin^{2} (φ)

sin^2(x)-2cos^2(x)=0

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

sin(x)= 1/(sqrt(10))

sin (x) = \frac{1}{10}

5 sec (θ) - 6 = 0

sec(x)=-1,-2pi<= x<= 2pi

sec (x) = - 1, - 2 π \leq x \leq 2 π