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受欢迎的三角函数 >

sqrt(3)csc^2(x)+2csc(x)=0

解答

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

解答

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: csc (x) = u

3 u^{2} + 2 u = 0

3 u^{2} + 2 u = 0 : u = 0, u = - \frac{2 3}{3}

3 u^{2} + 2 u = 0

使用求根公式求解

3 u^{2} + 2 u = 0

二次方程求根公式:

若

a = 3, b = 2, c = 0

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 3 \cdot 0}{2 3}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 3 \cdot 0}{2 3}

2^{2} - 43 \cdot 0 = 2

2^{2} - 43 \cdot 0

使用法则

0 \cdot a = 0

= 2^{2} - 0

2^{2} - 0 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 2

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

将解分隔开

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

u = \frac{- 2 + 2}{2 3} : 0

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

数字相加/相减:

- 2 + 2 = 0

= \frac{0}{2 3}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

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

\frac{- 2 - 2}{2 3}

数字相减:

- 2 - 2 = - 4

= \frac{- 4}{2 3}

使用分式法则:

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

= - \frac{4}{2 3}

数字相除:

\frac{4}{2} = 2

= - \frac{2}{3}

- \frac{2}{3}

有理化:

- \frac{2 3}{3}

- \frac{2}{3}

乘以共轭根式

\frac{3}{3}

= - \frac{2 3}{3 3}

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

二次方程组的解是:

u = 0, u = - \frac{2 3}{3}

u = csc (x)

代回

csc (x) = 0, csc (x) = - \frac{2 3}{3}

csc (x) = 0, csc (x) = - \frac{2 3}{3}

csc (x) = 0 :

无解

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

无解

csc (x) = - \frac{2 3}{3} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

csc (x) = - \frac{2 3}{3}

csc (x) = - \frac{2 3}{3}

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{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

合并所有解

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

7sin(2x)sin(x)=7cos(x)

7 sin (2 x) sin (x) = 7 cos (x)

csc(x)+cot(x)=3

csc (x) + cot (x) = 3

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

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

sin(x/2)=(sqrt(3))/2

sin (\frac{x}{2}) = \frac{3}{2}

cos(x)tan(x)-cos(x)=0

cos (x) tan (x) - cos (x) = 0