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 >

9tan^2(θ)-4=0

解答

9 tan^{2} (θ) - 4 = 0

解答

θ = 0.58800 \dots + πn, θ = - 0.58800 \dots + πn

+1

度数

θ = 33.69006 \dots^{\circ} + 18 0^{\circ} n, θ = - 33.69006 \dots^{\circ} + 18 0^{\circ} n

求解步骤

9 tan^{2} (θ) - 4 = 0

用替代法求解

9 tan^{2} (θ) - 4 = 0

令

: tan (θ) = u

9 u^{2} - 4 = 0

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

9 u^{2} - 4 = 0

将

4

到右边

9 u^{2} - 4 = 0

两边加上

4

9 u^{2} - 4 + 4 = 0 + 4

化简

9 u^{2} = 4

9 u^{2} = 4

两边除以

9

9 u^{2} = 4

两边除以

9

\frac{9 u ^{2}}{9} = \frac{4}{9}

化简

u^{2} = \frac{4}{9}

u^{2} = \frac{4}{9}

对于

x^{2} = f (a)

解为

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

u = \frac{4}{9}, u = - \frac{4}{9}

\frac{4}{9} = \frac{2}{3}

\frac{4}{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{4}{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{4}{3}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

- \frac{4}{9} = - \frac{2}{3}

- \frac{4}{9}

化简

\frac{4}{9} : \frac{2}{3}

\frac{4}{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{4}{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{4}{3}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

= - \frac{2}{3}

u = \frac{2}{3}, u = - \frac{2}{3}

u = tan (θ)

代回

tan (θ) = \frac{2}{3}, tan (θ) = - \frac{2}{3}

tan (θ) = \frac{2}{3}, tan (θ) = - \frac{2}{3}

tan (θ) = \frac{2}{3} : θ = arctan (\frac{2}{3}) + πn

tan (θ) = \frac{2}{3}

使用反三角函数性质

tan (θ) = \frac{2}{3}

tan (θ) = \frac{2}{3}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (\frac{2}{3}) + πn

θ = arctan (\frac{2}{3}) + πn

tan (θ) = - \frac{2}{3} : θ = arctan (- \frac{2}{3}) + πn

tan (θ) = - \frac{2}{3}

使用反三角函数性质

tan (θ) = - \frac{2}{3}

tan (θ) = - \frac{2}{3}

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- \frac{2}{3}) + πn

θ = arctan (- \frac{2}{3}) + πn

合并所有解

θ = arctan (\frac{2}{3}) + πn, θ = arctan (- \frac{2}{3}) + πn

以小数形式表示解

θ = 0.58800 \dots + πn, θ = - 0.58800 \dots + πn

作图

流行的例子

cos(x)=sqrt(1+sin(x))

cos (x) = 1 + sin (x)

cot (x - \frac{π}{4}) = - 1

3 cos (θ) + 1 = 1

sin (θ) = 3

sqrt(2)cos(x)csc(x)=2cos(x)

2 cos (x) csc (x) = 2 cos (x)