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 >

2sec^2(x)-5sec(x)+2=0,0<= x<= 360

解答

2 sec^{2} (x) - 5 sec (x) + 2 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

解答

x = 6 0^{\circ}, x = 30 0^{\circ}

+1

弧度

x = \frac{π}{3}, x = \frac{5 π}{3}

求解步骤

2 sec^{2} (x) - 5 sec (x) + 2 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

用替代法求解

2 sec^{2} (x) - 5 sec (x) + 2 = 0

令

: sec (x) = u

2 u^{2} - 5 u + 2 = 0

2 u^{2} - 5 u + 2 = 0 : u = 2, u = \frac{1}{2}

2 u^{2} - 5 u + 2 = 0

使用求根公式求解

2 u^{2} - 5 u + 2 = 0

二次方程求根公式:

若

a = 2, b = - 5, c = 2

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 \cdot 2}{2 \cdot 2}

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 \cdot 2}{2 \cdot 2}

(- 5)^{2} - 4 \cdot 2 \cdot 2 = 3

(- 5)^{2} - 4 \cdot 2 \cdot 2

使用指数法则:

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

若

n

是偶数

(- 5)^{2} = 5^{2}

= 5^{2} - 4 \cdot 2 \cdot 2

数字相乘:

4 \cdot 2 \cdot 2 = 16

= 5^{2} - 16

5^{2} = 25

= 25 - 16

数字相减:

25 - 16 = 9

= 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

u_{1, 2} = \frac{- ( - 5 ) \pm 3}{2 \cdot 2}

将解分隔开

u_{1} = \frac{- ( - 5 ) + 3}{2 \cdot 2}, u_{2} = \frac{- ( - 5 ) - 3}{2 \cdot 2}

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

\frac{- ( - 5 ) + 3}{2 \cdot 2}

使用法则

- (- a) = a

= \frac{5 + 3}{2 \cdot 2}

数字相加:

5 + 3 = 8

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

数字相乘:

2 \cdot 2 = 4

= \frac{8}{4}

数字相除:

\frac{8}{4} = 2

= 2

u = \frac{- ( - 5 ) - 3}{2 \cdot 2} : \frac{1}{2}

\frac{- ( - 5 ) - 3}{2 \cdot 2}

使用法则

- (- a) = a

= \frac{5 - 3}{2 \cdot 2}

数字相减:

5 - 3 = 2

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

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

约分:

2

= \frac{1}{2}

二次方程组的解是:

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

u = sec (x)

代回

sec (x) = 2, sec (x) = \frac{1}{2}

sec (x) = 2, sec (x) = \frac{1}{2}

sec (x) = 2, 0 \leq x \leq 36 0^{\circ} : x = 6 0^{\circ}, x = 30 0^{\circ}

sec (x) = 2, 0 \leq x \leq 36 0^{\circ}

sec (x) = 2

的通解

sec (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

在

0 \leq x \leq 36 0^{\circ}

范围内的解

x = 6 0^{\circ}, x = 30 0^{\circ}

sec (x) = \frac{1}{2}, 0 \leq x \leq 36 0^{\circ} :

无解

sec (x) = \frac{1}{2}, 0 \leq x \leq 36 0^{\circ}

sec (x) \leq - 1 or sec (x) \geq 1

无解

合并所有解

x = 6 0^{\circ}, x = 30 0^{\circ}

作图

流行的例子

2sin(5x)+sqrt(3)=0,0<= x<= 2pi

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

sin(2θ)=-24/25

sin (2 θ) = - \frac{24}{25}

sin(4x)+cos(4x)=1

sin (4 x) + cos (4 x) = 1

cos (A) = 0.7865

sin(x)=cos(2x+51)

sin (x) = cos (2 x + 5 1^{\circ})