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 >

-2tan^2(θ)-4tan(θ)+2=3tan(θ)+5

解答

- 2 tan^{2} (θ) - 4 tan (θ) + 2 = 3 tan (θ) + 5

解答

θ = - 1.24904 \dots + πn, θ = - 0.46364 \dots + πn

+1

度数

θ = - 71.56505 \dots^{\circ} + 18 0^{\circ} n, θ = - 26.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- 2 tan^{2} (θ) - 4 tan (θ) + 2 = 3 tan (θ) + 5

用替代法求解

- 2 tan^{2} (θ) - 4 tan (θ) + 2 = 3 tan (θ) + 5

令

: tan (θ) = u

- 2 u^{2} - 4 u + 2 = 3 u + 5

- 2 u^{2} - 4 u + 2 = 3 u + 5 : u = - 3, u = - \frac{1}{2}

- 2 u^{2} - 4 u + 2 = 3 u + 5

将

5

para o lado esquerdo

- 2 u^{2} - 4 u + 2 = 3 u + 5

两边减去

5

- 2 u^{2} - 4 u + 2 - 5 = 3 u + 5 - 5

化简

- 2 u^{2} - 4 u - 3 = 3 u

- 2 u^{2} - 4 u - 3 = 3 u

将

3 u

para o lado esquerdo

- 2 u^{2} - 4 u - 3 = 3 u

两边减去

3 u

- 2 u^{2} - 4 u - 3 - 3 u = 3 u - 3 u

化简

- 2 u^{2} - 7 u - 3 = 0

- 2 u^{2} - 7 u - 3 = 0

使用求根公式求解

- 2 u^{2} - 7 u - 3 = 0

二次方程求根公式:

若

a = - 2, b = - 7, c = - 3

u_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 ( - 2 ) ( - 3 )}{2 ( - 2 )}

u_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 ( - 2 ) ( - 3 )}{2 ( - 2 )}

(- 7)^{2} - 4 (- 2) (- 3) = 5

(- 7)^{2} - 4 (- 2) (- 3)

使用法则

- (- a) = a

= (- 7)^{2} - 4 \cdot 2 \cdot 3

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 7)^{2} = 7^{2}

= 7^{2} - 4 \cdot 2 \cdot 3

数字相乘:

4 \cdot 2 \cdot 3 = 24

= 7^{2} - 24

7^{2} = 49

= 49 - 24

数字相减:

49 - 24 = 25

= 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

u_{1, 2} = \frac{- ( - 7 ) \pm 5}{2 ( - 2 )}

将解分隔开

u_{1} = \frac{- ( - 7 ) + 5}{2 ( - 2 )}, u_{2} = \frac{- ( - 7 ) - 5}{2 ( - 2 )}

u = \frac{- ( - 7 ) + 5}{2 ( - 2 )} : - 3

\frac{- ( - 7 ) + 5}{2 ( - 2 )}

去除括号:

(- a) = - a, - (- a) = a

= \frac{7 + 5}{- 2 \cdot 2}

数字相加:

7 + 5 = 12

= \frac{12}{- 2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{12}{- 4}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{12}{4}

数字相除:

\frac{12}{4} = 3

= - 3

u = \frac{- ( - 7 ) - 5}{2 ( - 2 )} : - \frac{1}{2}

\frac{- ( - 7 ) - 5}{2 ( - 2 )}

去除括号:

(- a) = - a, - (- a) = a

= \frac{7 - 5}{- 2 \cdot 2}

数字相减:

7 - 5 = 2

= \frac{2}{- 2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{2}{- 4}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2}{4}

约分:

2

= - \frac{1}{2}

二次方程组的解是:

u = - 3, u = - \frac{1}{2}

u = tan (θ)

代回

tan (θ) = - 3, tan (θ) = - \frac{1}{2}

tan (θ) = - 3, tan (θ) = - \frac{1}{2}

tan (θ) = - 3 : θ = arctan (- 3) + πn

tan (θ) = - 3

使用反三角函数性质

tan (θ) = - 3

tan (θ) = - 3

的通解

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

θ = arctan (- 3) + πn

θ = arctan (- 3) + πn

tan (θ) = - \frac{1}{2} : θ = arctan (- \frac{1}{2}) + πn

tan (θ) = - \frac{1}{2}

使用反三角函数性质

tan (θ) = - \frac{1}{2}

tan (θ) = - \frac{1}{2}

的通解

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

θ = arctan (- \frac{1}{2}) + πn

θ = arctan (- \frac{1}{2}) + πn

合并所有解

θ = arctan (- 3) + πn, θ = arctan (- \frac{1}{2}) + πn

以小数形式表示解

θ = - 1.24904 \dots + πn, θ = - 0.46364 \dots + πn

作图

流行的例子

csc (3 x) = 1

solvefor x,cos(x+y)+cos(x)=0

so l v e f or x, cos (x + y) + cos (x) = 0

cos((pit)/2) pi/2 =0

cos (\frac{π t}{2}) \frac{π}{2} = 0

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

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

sin (x) = 0.653