zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

cot^2(θ)-9=0

解答

cot^{2} (θ) - 9 = 0

解答

θ = 0.32175 \dots + πn, θ = 2.81984 \dots + πn

+1

度数

θ = 18.43494 \dots^{\circ} + 18 0^{\circ} n, θ = 161.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

cot^{2} (θ) - 9 = 0

用替代法求解

cot^{2} (θ) - 9 = 0

令

: cot (θ) = u

u^{2} - 9 = 0

u^{2} - 9 = 0 : u = 3, u = - 3

u^{2} - 9 = 0

将

9

到右边

u^{2} - 9 = 0

两边加上

9

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

化简

u^{2} = 9

u^{2} = 9

对于

x^{2} = f (a)

解为

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

u = 9, u = - 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

- 9 = - 3

- 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

= - 3

u = 3, u = - 3

u = cot (θ)

代回

cot (θ) = 3, cot (θ) = - 3

cot (θ) = 3, cot (θ) = - 3

cot (θ) = 3 : θ = arccot (3) + πn

cot (θ) = 3

使用反三角函数性质

cot (θ) = 3

cot (θ) = 3

的通解

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

θ = arccot (3) + πn

θ = arccot (3) + πn

cot (θ) = - 3 : θ = arccot (- 3) + πn

cot (θ) = - 3

使用反三角函数性质

cot (θ) = - 3

cot (θ) = - 3

的通解

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

θ = arccot (- 3) + πn

θ = arccot (- 3) + πn

合并所有解

θ = arccot (3) + πn, θ = arccot (- 3) + πn

以小数形式表示解

θ = 0.32175 \dots + πn, θ = 2.81984 \dots + πn

作图

流行的例子

sec(x)=-1-tan(x)

sec (x) = - 1 - tan (x)

sec (θ) + 3 = 0

2sin(x)cos(x)+sqrt(3)sin(x)=0

2 sin (x) cos (x) + 3 sin (x) = 0

cos(2x)-cos(x)=0,0<= x<2pi

cos (2 x) - cos (x) = 0, 0 \leq x < 2 π

solvefor x,2cos(2x)-1=0

so l v e f or x, 2 cos (2 x) - 1 = 0