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受欢迎的三角函数 >

-4csc(x)=-csc^2(x)-4

解答

- 4 csc (x) = - csc^{2} (x) - 4

解答

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

+1

度数

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

求解步骤

- 4 csc (x) = - csc^{2} (x) - 4

用替代法求解

- 4 csc (x) = - csc^{2} (x) - 4

令

: csc (x) = u

- 4 u = - u^{2} - 4

- 4 u = - u^{2} - 4 : u = 2

- 4 u = - u^{2} - 4

交换两边

- u^{2} - 4 = - 4 u

将

4 u

para o lado esquerdo

- u^{2} - 4 = - 4 u

两边加上

4 u

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

化简

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

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

改写成标准形式

a x^{2} + b x + c = 0

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

使用求根公式求解

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

二次方程求根公式:

若

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

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

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

4^{2} - 4 (- 1) (- 4) = 0

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

使用法则

- (- a) = a

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

数字相乘:

4 \cdot 1 \cdot 4 = 16

= 4^{2} - 16

4^{2} = 16

= 16 - 16

数字相减:

16 - 16 = 0

= 0

u_{1, 2} = \frac{- 4 \pm 0}{2 ( - 1 )}

u = \frac{- 4}{2 ( - 1 )}

\frac{- 4}{2 ( - 1 )} = 2

\frac{- 4}{2 ( - 1 )}

去除括号:

(- a) = - a

= \frac{- 4}{- 2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 4}{- 2}

使用分式法则:

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

= \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= 2

u = 2

二次方程组的解是:

u = 2

u = csc (x)

代回

csc (x) = 2

csc (x) = 2

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = 2

csc (x) = 2

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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

合并所有解

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

作图

流行的例子

csc(7x+3)=sqrt(2)

csc (7 x + 3) = 2

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18sin(x)=18cos(x)

18 sin (x) = 18 cos (x)

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