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 >

9sec^2(x)-9sec(x)=18

解答

9 sec^{2} (x) - 9 sec (x) = 18

解答

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

9 sec^{2} (x) - 9 sec (x) = 18

用替代法求解

9 sec^{2} (x) - 9 sec (x) = 18

令

: sec (x) = u

9 u^{2} - 9 u = 18

9 u^{2} - 9 u = 18 : u = 2, u = - 1

9 u^{2} - 9 u = 18

将

18

para o lado esquerdo

9 u^{2} - 9 u = 18

两边减去

18

9 u^{2} - 9 u - 18 = 18 - 18

化简

9 u^{2} - 9 u - 18 = 0

9 u^{2} - 9 u - 18 = 0

使用求根公式求解

9 u^{2} - 9 u - 18 = 0

二次方程求根公式:

若

a = 9, b = - 9, c = - 18

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 9 ( - 18 )}{2 \cdot 9}

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 9 ( - 18 )}{2 \cdot 9}

(- 9)^{2} - 4 \cdot 9 (- 18) = 27

(- 9)^{2} - 4 \cdot 9 (- 18)

使用法则

- (- a) = a

= (- 9)^{2} + 4 \cdot 9 \cdot 18

使用指数法则:

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

若

n

是偶数

(- 9)^{2} = 9^{2}

= 9^{2} + 4 \cdot 9 \cdot 18

数字相乘:

4 \cdot 9 \cdot 18 = 648

= 9^{2} + 648

9^{2} = 81

= 81 + 648

数字相加:

81 + 648 = 729

= 729

因式分解数字:

729 = 2 7^{2}

= 2 7^{2}

使用根式运算法则:

n a^{n} = a

2 7^{2} = 27

= 27

u_{1, 2} = \frac{- ( - 9 ) \pm 27}{2 \cdot 9}

将解分隔开

u_{1} = \frac{- ( - 9 ) + 27}{2 \cdot 9}, u_{2} = \frac{- ( - 9 ) - 27}{2 \cdot 9}

u = \frac{- ( - 9 ) + 27}{2 \cdot 9} : 2

\frac{- ( - 9 ) + 27}{2 \cdot 9}

使用法则

- (- a) = a

= \frac{9 + 27}{2 \cdot 9}

数字相加:

9 + 27 = 36

= \frac{36}{2 \cdot 9}

数字相乘:

2 \cdot 9 = 18

= \frac{36}{18}

数字相除:

\frac{36}{18} = 2

= 2

u = \frac{- ( - 9 ) - 27}{2 \cdot 9} : - 1

\frac{- ( - 9 ) - 27}{2 \cdot 9}

使用法则

- (- a) = a

= \frac{9 - 27}{2 \cdot 9}

数字相减:

9 - 27 = - 18

= \frac{- 18}{2 \cdot 9}

数字相乘:

2 \cdot 9 = 18

= \frac{- 18}{18}

使用分式法则:

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

= - \frac{18}{18}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = 2, u = - 1

u = sec (x)

代回

sec (x) = 2, sec (x) = - 1

sec (x) = 2, sec (x) = - 1

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = 2

sec (x) = 2

的通解

sec (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - 1 : x = π + 2 πn

sec (x) = - 1

sec (x) = - 1

的通解

sec (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = π + 2 πn

x = π + 2 πn

合并所有解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

作图

流行的例子

sec^2(x)-8sec(-x)-20=0

sec^{2} (x) - 8 sec (- x) - 20 = 0

3arccos(5x)=2pi

3 arccos (5 x) = 2 π

sqrt(3)cot(3θ+pi/3)+1=0

3 cot (3 θ + \frac{π}{3}) + 1 = 0

tan (θ) = \frac{4}{13}

2cos^2(x)-cos(x)-1=0,0<= x<= 2pi

2 cos^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq 2 π