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 >

25cot^2(θ)-16=0

解答

25 cot^{2} (θ) - 16 = 0

解答

θ = 0.89605 \dots + πn, θ = 2.24553 \dots + πn

+1

度数

θ = 51.34019 \dots^{\circ} + 18 0^{\circ} n, θ = 128.65980 \dots^{\circ} + 18 0^{\circ} n

求解步骤

25 cot^{2} (θ) - 16 = 0

用替代法求解

25 cot^{2} (θ) - 16 = 0

令

: cot (θ) = u

25 u^{2} - 16 = 0

25 u^{2} - 16 = 0 : u = \frac{4}{5}, u = - \frac{4}{5}

25 u^{2} - 16 = 0

将

16

到右边

25 u^{2} - 16 = 0

两边加上

16

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

化简

25 u^{2} = 16

25 u^{2} = 16

两边除以

25

25 u^{2} = 16

两边除以

25

\frac{25 u ^{2}}{25} = \frac{16}{25}

化简

u^{2} = \frac{16}{25}

u^{2} = \frac{16}{25}

对于

x^{2} = f (a)

解为

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

u = \frac{16}{25}, u = - \frac{16}{25}

\frac{16}{25} = \frac{4}{5}

\frac{16}{25}

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}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{16}{5}

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}{5}

- \frac{16}{25} = - \frac{4}{5}

- \frac{16}{25}

化简

\frac{16}{25} : \frac{4}{5}

\frac{16}{25}

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}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{16}{5}

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}{5}

= - \frac{4}{5}

u = \frac{4}{5}, u = - \frac{4}{5}

u = cot (θ)

代回

cot (θ) = \frac{4}{5}, cot (θ) = - \frac{4}{5}

cot (θ) = \frac{4}{5}, cot (θ) = - \frac{4}{5}

cot (θ) = \frac{4}{5} : θ = arccot (\frac{4}{5}) + πn

cot (θ) = \frac{4}{5}

使用反三角函数性质

cot (θ) = \frac{4}{5}

cot (θ) = \frac{4}{5}

的通解

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

θ = arccot (\frac{4}{5}) + πn

θ = arccot (\frac{4}{5}) + πn

cot (θ) = - \frac{4}{5} : θ = arccot (- \frac{4}{5}) + πn

cot (θ) = - \frac{4}{5}

使用反三角函数性质

cot (θ) = - \frac{4}{5}

cot (θ) = - \frac{4}{5}

的通解

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

θ = arccot (- \frac{4}{5}) + πn

θ = arccot (- \frac{4}{5}) + πn

合并所有解

θ = arccot (\frac{4}{5}) + πn, θ = arccot (- \frac{4}{5}) + πn

以小数形式表示解

θ = 0.89605 \dots + πn, θ = 2.24553 \dots + πn

作图

流行的例子

2sin^2(x)=sin(x)+1

2 sin^{2} (x) = sin (x) + 1

sin(3x)=-(sqrt(3))/2

sin (3 x) = - \frac{3}{2}

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

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

3sin(x)+csc(x)=0

3 sin (x) + csc (x) = 0

cos (x) = \frac{4}{7}