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受欢迎的三角函数 >

solvefor 3cot^2(x)-1=0,x

解答

求解

3 cot^{2} (x) - 1 = 0, x

解答

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

+1

度数

x = 6 0^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 18 0^{\circ} n

求解步骤

3 cot^{2} (x) - 1 = 0

用替代法求解

3 cot^{2} (x) - 1 = 0

令

: cot (x) = u

3 u^{2} - 1 = 0

3 u^{2} - 1 = 0 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} - 1 = 0

将

1

到右边

3 u^{2} - 1 = 0

两边加上

1

3 u^{2} - 1 + 1 = 0 + 1

化简

3 u^{2} = 1

3 u^{2} = 1

两边除以

3

3 u^{2} = 1

两边除以

3

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

化简

u^{2} = \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 (x)

代回

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

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

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

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

使用反三角函数性质

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

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

的通解

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

x = arccot (\frac{1}{3}) + πn

x = arccot (\frac{1}{3}) + πn

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

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

使用反三角函数性质

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

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

的通解

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

x = arccot (- \frac{1}{3}) + πn

x = arccot (- \frac{1}{3}) + πn

合并所有解

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

以小数形式表示解

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

作图

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