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受欢迎的三角函数 >

8sec^2(x)-8sec(x)=16

解答

8 sec^{2} (x) - 8 sec (x) = 16

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

8 sec^{2} (x) - 8 sec (x) = 16

用替代法求解

8 sec^{2} (x) - 8 sec (x) = 16

令

: sec (x) = u

8 u^{2} - 8 u = 16

8 u^{2} - 8 u = 16 : u = 2, u = - 1

8 u^{2} - 8 u = 16

将

16

para o lado esquerdo

8 u^{2} - 8 u = 16

两边减去

16

8 u^{2} - 8 u - 16 = 16 - 16

化简

8 u^{2} - 8 u - 16 = 0

8 u^{2} - 8 u - 16 = 0

使用求根公式求解

8 u^{2} - 8 u - 16 = 0

二次方程求根公式:

若

a = 8, b = - 8, c = - 16

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 8 ( - 16 )}{2 \cdot 8}

u_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 8 ( - 16 )}{2 \cdot 8}

(- 8)^{2} - 4 \cdot 8 (- 16) = 24

(- 8)^{2} - 4 \cdot 8 (- 16)

使用法则

- (- a) = a

= (- 8)^{2} + 4 \cdot 8 \cdot 16

使用指数法则:

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

若

n

是偶数

(- 8)^{2} = 8^{2}

= 8^{2} + 4 \cdot 8 \cdot 16

数字相乘:

4 \cdot 8 \cdot 16 = 512

= 8^{2} + 512

8^{2} = 64

= 64 + 512

数字相加:

64 + 512 = 576

= 576

因式分解数字:

576 = 2 4^{2}

= 2 4^{2}

使用根式运算法则:

n a^{n} = a

2 4^{2} = 24

= 24

u_{1, 2} = \frac{- ( - 8 ) \pm 24}{2 \cdot 8}

将解分隔开

u_{1} = \frac{- ( - 8 ) + 24}{2 \cdot 8}, u_{2} = \frac{- ( - 8 ) - 24}{2 \cdot 8}

u = \frac{- ( - 8 ) + 24}{2 \cdot 8} : 2

\frac{- ( - 8 ) + 24}{2 \cdot 8}

使用法则

- (- a) = a

= \frac{8 + 24}{2 \cdot 8}

数字相加:

8 + 24 = 32

= \frac{32}{2 \cdot 8}

数字相乘:

2 \cdot 8 = 16

= \frac{32}{16}

数字相除:

\frac{32}{16} = 2

= 2

u = \frac{- ( - 8 ) - 24}{2 \cdot 8} : - 1

\frac{- ( - 8 ) - 24}{2 \cdot 8}

使用法则

- (- a) = a

= \frac{8 - 24}{2 \cdot 8}

数字相减:

8 - 24 = - 16

= \frac{- 16}{2 \cdot 8}

数字相乘:

2 \cdot 8 = 16

= \frac{- 16}{16}

使用分式法则:

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

= - \frac{16}{16}

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

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50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14

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