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受欢迎的三角函数 >

9cot^2(θ)-16=0

解答

9 cot^{2} (θ) - 16 = 0

解答

θ = 0.64350 \dots + πn, θ = 2.49809 \dots + πn

+1

度数

θ = 36.86989 \dots^{\circ} + 18 0^{\circ} n, θ = 143.13010 \dots^{\circ} + 18 0^{\circ} n

求解步骤

9 cot^{2} (θ) - 16 = 0

用替代法求解

9 cot^{2} (θ) - 16 = 0

令

: cot (θ) = u

9 u^{2} - 16 = 0

9 u^{2} - 16 = 0 : u = \frac{4}{3}, u = - \frac{4}{3}

9 u^{2} - 16 = 0

将

16

到右边

9 u^{2} - 16 = 0

两边加上

16

9 u^{2} - 16 + 16 = 0 + 16

化简

9 u^{2} = 16

9 u^{2} = 16

两边除以

9

9 u^{2} = 16

两边除以

9

\frac{9 u ^{2}}{9} = \frac{16}{9}

化简

u^{2} = \frac{16}{9}

u^{2} = \frac{16}{9}

对于

x^{2} = f (a)

解为

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

u = \frac{16}{9}, u = - \frac{16}{9}

\frac{16}{9} = \frac{4}{3}

\frac{16}{9}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{16}{9}

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

= \frac{16}{3}

16 = 4

16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

= \frac{4}{3}

- \frac{16}{9} = - \frac{4}{3}

- \frac{16}{9}

化简

\frac{16}{9} : \frac{4}{3}

\frac{16}{9}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{16}{9}

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

= \frac{16}{3}

16 = 4

16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

= \frac{4}{3}

= - \frac{4}{3}

u = \frac{4}{3}, u = - \frac{4}{3}

u = cot (θ)

代回

cot (θ) = \frac{4}{3}, cot (θ) = - \frac{4}{3}

cot (θ) = \frac{4}{3}, cot (θ) = - \frac{4}{3}

cot (θ) = \frac{4}{3} : θ = arccot (\frac{4}{3}) + πn

cot (θ) = \frac{4}{3}

使用反三角函数性质

cot (θ) = \frac{4}{3}

cot (θ) = \frac{4}{3}

的通解

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

θ = arccot (\frac{4}{3}) + πn

θ = arccot (\frac{4}{3}) + πn

cot (θ) = - \frac{4}{3} : θ = arccot (- \frac{4}{3}) + πn

cot (θ) = - \frac{4}{3}

使用反三角函数性质

cot (θ) = - \frac{4}{3}

cot (θ) = - \frac{4}{3}

的通解

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

θ = arccot (- \frac{4}{3}) + πn

θ = arccot (- \frac{4}{3}) + πn

合并所有解

θ = arccot (\frac{4}{3}) + πn, θ = arccot (- \frac{4}{3}) + πn

以小数形式表示解

θ = 0.64350 \dots + πn, θ = 2.49809 \dots + πn

作图

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