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受欢迎的三角函数 >

sqrt(3)cot(pi/2 x)=-3

解答

3 cot (\frac{π}{2} x) = - 3

解答

x = \frac{5}{3} + 2 n

+1

度数

x = 95.49296 \dots^{\circ} + 114.59155 \dots^{\circ} n

求解步骤

3 cot (\frac{π}{2} x) = - 3

两边除以

3

3 cot (\frac{π}{2} x) = - 3

两边除以

3

\frac{3 cot ( \frac{π}{2} x )}{3} = \frac{- 3}{3}

化简

\frac{3 cot ( \frac{π}{2} x )}{3} = \frac{- 3}{3}

化简

\frac{3 cot ( \frac{π}{2} x )}{3} : cot (\frac{π}{2} x)

\frac{3 cot ( \frac{π}{2} x )}{3}

约分:

3

= cot (\frac{π}{2} x)

化简

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

\frac{- 3}{3}

使用分式法则:

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

= - \frac{3}{3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

使用指数法则:

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

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

数字相减:

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

= 3^{\frac{1}{2}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= - 3

cot (\frac{π}{2} x) = - 3

cot (\frac{π}{2} x) = - 3

cot (\frac{π}{2} x) = - 3

cot (\frac{π}{2} x) = - 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

\frac{π}{2} x = \frac{5 π}{6} + πn

\frac{π}{2} x = \frac{5 π}{6} + πn

解

\frac{π}{2} x = \frac{5 π}{6} + πn : x = \frac{5}{3} + 2 n

\frac{π}{2} x = \frac{5 π}{6} + πn

在两边乘以

2

\frac{π}{2} x = \frac{5 π}{6} + πn

在两边乘以

2

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

化简

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

化简

2 \cdot \frac{π}{2} x : π x

2 \cdot \frac{π}{2} x

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π}{2} x

约分:

2

= x π

化简

2 \cdot \frac{5 π}{6} + 2 πn : \frac{5 π}{3} + 2 πn

2 \cdot \frac{5 π}{6} + 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π 2}{6}

数字相乘:

5 \cdot 2 = 10

= \frac{10 π}{6}

约分:

2

= \frac{5 π}{3}

= \frac{5 π}{3} + 2 πn

π x = \frac{5 π}{3} + 2 πn

π x = \frac{5 π}{3} + 2 πn

π x = \frac{5 π}{3} + 2 πn

两边除以

π

π x = \frac{5 π}{3} + 2 πn

两边除以

π

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

化简

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

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{5 π}{3}}{π} + \frac{2 πn}{π} : \frac{5}{3} + 2 n

\frac{\frac{5 π}{3}}{π} + \frac{2 πn}{π}

\frac{\frac{5 π}{3}}{π} = \frac{5}{3}

\frac{\frac{5 π}{3}}{π}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{3 π}

约分:

π

= \frac{5}{3}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= \frac{5}{3} + 2 n

x = \frac{5}{3} + 2 n

x = \frac{5}{3} + 2 n

x = \frac{5}{3} + 2 n

x = \frac{5}{3} + 2 n

作图

流行的例子

cos(θ)= 3/5 ,(3pi)/2 <θ<2pi

cos (θ) = \frac{3}{5}, \frac{3 π}{2} < θ < 2 π

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

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

-3cos(2θ)+2sin(θ)+5=9sin(θ)

- 3 cos (2 θ) + 2 sin (θ) + 5 = 9 sin (θ)

3+sin(x)=5cos(2x)

3 + sin (x) = 5 cos (2 x)

cos (x) = \frac{15}{20}