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受欢迎的三角函数 >

cot^2(2x-pi/3)= 1/3

解答

cot^{2} (2 x - \frac{π}{3}) = \frac{1}{3}

解答

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

+1

度数

x = 6 0^{\circ} + 9 0^{\circ} n, x = 9 0^{\circ} + 9 0^{\circ} n

求解步骤

cot^{2} (2 x - \frac{π}{3}) = \frac{1}{3}

用替代法求解

cot^{2} (2 x - \frac{π}{3}) = \frac{1}{3}

令

: cot (2 x - \frac{π}{3}) = u

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

u^{2} = \frac{1}{3} : u = \frac{1}{3}, u = - \frac{1}{3}

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

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{1}{3}, u = - \frac{1}{3}

u = cot (2 x - \frac{π}{3})

代回

cot (2 x - \frac{π}{3}) = \frac{1}{3}, cot (2 x - \frac{π}{3}) = - \frac{1}{3}

cot (2 x - \frac{π}{3}) = \frac{1}{3}, cot (2 x - \frac{π}{3}) = - \frac{1}{3}

cot (2 x - \frac{π}{3}) = \frac{1}{3} : x = \frac{π}{3} + \frac{πn}{2}

cot (2 x - \frac{π}{3}) = \frac{1}{3}

使用反三角函数性质

cot (2 x - \frac{π}{3}) = \frac{1}{3}

cot (2 x - \frac{π}{3}) = \frac{1}{3}

的通解

cot (x) = a \Rightarrow x = arccot (a) + πn

2 x - \frac{π}{3} = arccot (\frac{1}{3}) + πn

2 x - \frac{π}{3} = arccot (\frac{1}{3}) + πn

解

2 x - \frac{π}{3} = arccot (\frac{1}{3}) + πn : x = \frac{π}{3} + \frac{πn}{2}

2 x - \frac{π}{3} = arccot (\frac{1}{3}) + πn

化简

arccot (\frac{1}{3}) + πn : \frac{π}{3} + πn

arccot (\frac{1}{3}) + πn

使用以下普通恒等式:

arccot (\frac{1}{3}) = \frac{π}{3}

x - 3 - 1 - \frac{3}{3} 0 \frac{3}{3} 13 arccot (x) \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} arccot (x) 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ}

= \frac{π}{3} + πn

2 x - \frac{π}{3} = \frac{π}{3} + πn

将

\frac{π}{3}

到右边

2 x - \frac{π}{3} = \frac{π}{3} + πn

两边加上

\frac{π}{3}

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

化简

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

化简

2 x - \frac{π}{3} + \frac{π}{3} : 2 x

2 x - \frac{π}{3} + \frac{π}{3}

同类项相加:

- \frac{π}{3} + \frac{π}{3} = 0

= 2 x

化简

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

\frac{π}{3} + πn + \frac{π}{3}

对同类项分组

= \frac{π}{3} + \frac{π}{3} + πn

合并分式

\frac{π}{3} + \frac{π}{3} : \frac{2 π}{3}

使用法则

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

= \frac{π + π}{3}

同类项相加:

π + π = 2 π

= \frac{2 π}{3}

= \frac{2 π}{3} + πn

2 x = \frac{2 π}{3} + πn

2 x = \frac{2 π}{3} + πn

2 x = \frac{2 π}{3} + πn

两边除以

2

2 x = \frac{2 π}{3} + πn

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

使用分式法则:

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

= \frac{2 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{2 π}{6}

约分:

2

= \frac{π}{3}

= \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}

cot (2 x - \frac{π}{3}) = - \frac{1}{3} : x = \frac{πn}{2} + \frac{π}{2}

cot (2 x - \frac{π}{3}) = - \frac{1}{3}

使用反三角函数性质

cot (2 x - \frac{π}{3}) = - \frac{1}{3}

cot (2 x - \frac{π}{3}) = - \frac{1}{3}

的通解

cot (x) = - a \Rightarrow x = arccot (- a) + πn

2 x - \frac{π}{3} = arccot (- \frac{1}{3}) + πn

2 x - \frac{π}{3} = arccot (- \frac{1}{3}) + πn

解

2 x - \frac{π}{3} = arccot (- \frac{1}{3}) + πn : x = \frac{πn}{2} + \frac{π}{2}

2 x - \frac{π}{3} = arccot (- \frac{1}{3}) + πn

化简

arccot (- \frac{1}{3}) + πn : \frac{2 π}{3} + πn

arccot (- \frac{1}{3}) + πn

使用以下普通恒等式:

arccot (- \frac{1}{3}) = \frac{2 π}{3}

x - 3 - 1 - \frac{3}{3} 0 \frac{3}{3} 13 arccot (x) \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} arccot (x) 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ}

= \frac{2 π}{3} + πn

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

将

\frac{π}{3}

到右边

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

两边加上

\frac{π}{3}

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

化简

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

化简

2 x - \frac{π}{3} + \frac{π}{3} : 2 x

2 x - \frac{π}{3} + \frac{π}{3}

同类项相加:

- \frac{π}{3} + \frac{π}{3} = 0

= 2 x

化简

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

\frac{2 π}{3} + πn + \frac{π}{3}

对同类项分组

= πn + \frac{π}{3} + \frac{2 π}{3}

合并分式

\frac{π}{3} + \frac{2 π}{3} : π

使用法则

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

= \frac{π + 2 π}{3}

同类项相加:

π + 2 π = 3 π

= \frac{3 π}{3}

数字相除:

\frac{3}{3} = 1

= π

= πn + π

2 x = πn + π

2 x = πn + π

2 x = πn + π

两边除以

2

2 x = πn + π

两边除以

2

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

化简

x = \frac{πn}{2} + \frac{π}{2}

x = \frac{πn}{2} + \frac{π}{2}

x = \frac{πn}{2} + \frac{π}{2}

合并所有解

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

作图

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