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受欢迎的三角函数 >

4csc(x)=sqrt(3)csc(x)cot(x)+3csc(x)

解答

4 csc (x) = 3 csc (x) cot (x) + 3 csc (x)

解答

x = \frac{π}{3} + πn

+1

度数

x = 6 0^{\circ} + 18 0^{\circ} n

求解步骤

4 csc (x) = 3 csc (x) cot (x) + 3 csc (x)

两边减去

3 csc (x) cot (x) + 3 csc (x)

csc (x) - 3 csc (x) cot (x) = 0

分解

csc (x) - 3 csc (x) cot (x) : csc (x) (1 - 3 cot (x))

csc (x) - 3 csc (x) cot (x)

因式分解出通项

csc (x)

= csc (x) (1 - 3 cot (x))

csc (x) (1 - 3 cot (x)) = 0

分别求解每个部分

csc (x) = 0 or 1 - 3 cot (x) = 0

csc (x) = 0 :

无解

csc (x) = 0

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

无解

1 - 3 cot (x) = 0 : x = \frac{π}{3} + πn

1 - 3 cot (x) = 0

将

1

到右边

1 - 3 cot (x) = 0

两边减去

1

1 - 3 cot (x) - 1 = 0 - 1

化简

- 3 cot (x) = - 1

- 3 cot (x) = - 1

两边除以

- 3

- 3 cot (x) = - 1

两边除以

- 3

\frac{- 3 cot ( x )}{- 3} = \frac{- 1}{- 3}

化简

\frac{- 3 cot ( x )}{- 3} = \frac{- 1}{- 3}

化简

\frac{- 3 cot ( x )}{- 3} : cot (x)

\frac{- 3 cot ( x )}{- 3}

使用分式法则:

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

= \frac{3 cot ( x )}{3}

约分:

3

= cot (x)

化简

\frac{- 1}{- 3} : \frac{3}{3}

\frac{- 1}{- 3}

使用分式法则:

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

= \frac{1}{3}

\frac{1}{3}

有理化:

\frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

的通解

cot (x)

周期表（周期为

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

合并所有解

x = \frac{π}{3} + πn

作图

流行的例子

4cos^2(x)+4cos(x)=1,0<= x<360

4 cos^{2} (x) + 4 cos (x) = 1, 0^{\circ} \leq x < 36 0^{\circ}

8 cos^{2} (x) = 4

4 cos (3 x) = 0

sin^2(x)=sin^2(x/2)

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

cos (x) = \frac{6}{8}