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受欢迎的三角函数 >

3cot^2(θ)-1=0

解答

3 cot^{2} (θ) - 1 = 0

解答

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

+1

度数

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

求解步骤

3 cot^{2} (θ) - 1 = 0

用替代法求解

3 cot^{2} (θ) - 1 = 0

令

: cot (θ) = 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 (θ)

代回

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

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

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

cot (θ) = \frac{1}{3}

使用反三角函数性质

cot (θ) = \frac{1}{3}

cot (θ) = \frac{1}{3}

的通解

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

θ = arccot (\frac{1}{3}) + πn

θ = arccot (\frac{1}{3}) + πn

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

cot (θ) = - \frac{1}{3}

使用反三角函数性质

cot (θ) = - \frac{1}{3}

cot (θ) = - \frac{1}{3}

的通解

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

θ = arccot (- \frac{1}{3}) + πn

θ = arccot (- \frac{1}{3}) + πn

合并所有解

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

以小数形式表示解

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

作图

流行的例子

tan(x/7)+sqrt(3)=0

tan (\frac{x}{7}) + 3 = 0

3(tan(θ)-2)=2tan(θ)-7

3 (tan (θ) - 2) = 2 tan (θ) - 7

sqrt(3)tan(θ)+1=0,0<= θ<= 2pi

3 tan (θ) + 1 = 0, 0 \leq θ \leq 2 π

tan(x)=tan^2(x)

tan (x) = tan^{2} (x)

solvefor y,sin(xy)=x

so l v e f or y, sin (x y) = x