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 >

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

解答

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

解答

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n, x = 104.47751 \dots^{\circ} + 36 0^{\circ} n, x = - 104.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: sec (x) = u

u^{2} + 2 u - 8 = 0

u^{2} + 2 u - 8 = 0 : u = 2, u = - 4

u^{2} + 2 u - 8 = 0

使用求根公式求解

u^{2} + 2 u - 8 = 0

二次方程求根公式:

若

a = 1, b = 2, c = - 8

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

2^{2} - 4 \cdot 1 \cdot (- 8) = 6

2^{2} - 4 \cdot 1 \cdot (- 8)

使用法则

- (- a) = a

= 2^{2} + 4 \cdot 1 \cdot 8

数字相乘:

4 \cdot 1 \cdot 8 = 32

= 2^{2} + 32

2^{2} = 4

= 4 + 32

数字相加:

4 + 32 = 36

= 36

因式分解数字:

36 = 6^{2}

= 6^{2}

使用根式运算法则:

n a^{n} = a

6^{2} = 6

= 6

u_{1, 2} = \frac{- 2 \pm 6}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- 2 + 6}{2 \cdot 1}, u_{2} = \frac{- 2 - 6}{2 \cdot 1}

u = \frac{- 2 + 6}{2 \cdot 1} : 2

\frac{- 2 + 6}{2 \cdot 1}

数字相加/相减:

- 2 + 6 = 4

= \frac{4}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= 2

u = \frac{- 2 - 6}{2 \cdot 1} : - 4

\frac{- 2 - 6}{2 \cdot 1}

数字相减:

- 2 - 6 = - 8

= \frac{- 8}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 8}{2}

使用分式法则:

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

= - \frac{8}{2}

数字相除:

\frac{8}{2} = 4

= - 4

二次方程组的解是:

u = 2, u = - 4

u = sec (x)

代回

sec (x) = 2, sec (x) = - 4

sec (x) = 2, sec (x) = - 4

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) = - 4 : x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

sec (x) = - 4

使用反三角函数性质

sec (x) = - 4

sec (x) = - 4

的通解

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

合并所有解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

以小数形式表示解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

作图

流行的例子

3cos^2(x)+4sin(x)-4=0

3 cos^{2} (x) + 4 sin (x) - 4 = 0

sin (x) = \frac{7}{15}

-4sin(x)=-cos^2(x)+4,0<= x<= 2pi

- 4 sin (x) = - cos^{2} (x) + 4, 0 \leq x \leq 2 π

sin(2x)cot(x)=0

sin (2 x) cot (x) = 0

3sec(θ)-2sqrt(3)=0

3 sec (θ) - 23 = 0