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受欢迎的三角函数 >

5sec^2(x)-5sec(x)=10

解答

5 sec^{2} (x) - 5 sec (x) = 10

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

5 sec^{2} (x) - 5 sec (x) = 10

用替代法求解

5 sec^{2} (x) - 5 sec (x) = 10

令

: sec (x) = u

5 u^{2} - 5 u = 10

5 u^{2} - 5 u = 10 : u = 2, u = - 1

5 u^{2} - 5 u = 10

将

10

para o lado esquerdo

5 u^{2} - 5 u = 10

两边减去

10

5 u^{2} - 5 u - 10 = 10 - 10

化简

5 u^{2} - 5 u - 10 = 0

5 u^{2} - 5 u - 10 = 0

使用求根公式求解

5 u^{2} - 5 u - 10 = 0

二次方程求根公式:

若

a = 5, b = - 5, c = - 10

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 5 ( - 10 )}{2 \cdot 5}

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 5 ( - 10 )}{2 \cdot 5}

(- 5)^{2} - 4 \cdot 5 (- 10) = 15

(- 5)^{2} - 4 \cdot 5 (- 10)

使用法则

- (- a) = a

= (- 5)^{2} + 4 \cdot 5 \cdot 10

使用指数法则:

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

若

n

是偶数

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

= 5^{2} + 4 \cdot 5 \cdot 10

数字相乘:

4 \cdot 5 \cdot 10 = 200

= 5^{2} + 200

5^{2} = 25

= 25 + 200

数字相加:

25 + 200 = 225

= 225

因式分解数字:

225 = 1 5^{2}

= 1 5^{2}

使用根式运算法则:

n a^{n} = a

1 5^{2} = 15

= 15

u_{1, 2} = \frac{- ( - 5 ) \pm 15}{2 \cdot 5}

将解分隔开

u_{1} = \frac{- ( - 5 ) + 15}{2 \cdot 5}, u_{2} = \frac{- ( - 5 ) - 15}{2 \cdot 5}

u = \frac{- ( - 5 ) + 15}{2 \cdot 5} : 2

\frac{- ( - 5 ) + 15}{2 \cdot 5}

使用法则

- (- a) = a

= \frac{5 + 15}{2 \cdot 5}

数字相加:

5 + 15 = 20

= \frac{20}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{20}{10}

数字相除:

\frac{20}{10} = 2

= 2

u = \frac{- ( - 5 ) - 15}{2 \cdot 5} : - 1

\frac{- ( - 5 ) - 15}{2 \cdot 5}

使用法则

- (- a) = a

= \frac{5 - 15}{2 \cdot 5}

数字相减:

5 - 15 = - 10

= \frac{- 10}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{- 10}{10}

使用分式法则:

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

= - \frac{10}{10}

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

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