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受欢迎的三角函数 >

-1=-4sec(y)-sec^2(y)-5

解答

- 1 = - 4 sec (y) - sec^{2} (y) - 5

解答

y = \frac{2 π}{3} + 2 πn, y = \frac{4 π}{3} + 2 πn

+1

度数

y = 12 0^{\circ} + 36 0^{\circ} n, y = 24 0^{\circ} + 36 0^{\circ} n

求解步骤

- 1 = - 4 sec (y) - sec^{2} (y) - 5

交换两边

- 4 sec (y) - sec^{2} (y) - 5 = - 1

用替代法求解

- 4 sec (y) - sec^{2} (y) - 5 = - 1

令

: sec (y) = u

- 4 u - u^{2} - 5 = - 1

- 4 u - u^{2} - 5 = - 1 : u = - 2

- 4 u - u^{2} - 5 = - 1

将

1

para o lado esquerdo

- 4 u - u^{2} - 5 = - 1

两边加上

1

- 4 u - u^{2} - 5 + 1 = - 1 + 1

化简

- u^{2} - 4 u - 4 = 0

- u^{2} - 4 u - 4 = 0

使用求根公式求解

- u^{2} - 4 u - 4 = 0

二次方程求根公式:

若

a = - 1, b = - 4, c = - 4

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

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

(- 4)^{2} - 4 (- 1) (- 4) = 0

(- 4)^{2} - 4 (- 1) (- 4)

使用法则

- (- a) = a

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

使用指数法则:

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

若

n

是偶数

(- 4)^{2} = 4^{2}

= 4^{2} - 4 \cdot 1 \cdot 4

数字相乘:

4 \cdot 1 \cdot 4 = 16

= 4^{2} - 16

4^{2} = 16

= 16 - 16

数字相减:

16 - 16 = 0

= 0

u_{1, 2} = \frac{- ( - 4 ) \pm 0}{2 ( - 1 )}

u = \frac{- ( - 4 )}{2 ( - 1 )}

\frac{- ( - 4 )}{2 ( - 1 )} = - 2

\frac{- ( - 4 )}{2 ( - 1 )}

去除括号:

(- a) = - a, - (- a) = a

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

数字相乘:

2 \cdot 1 = 2

= \frac{4}{- 2}

使用分式法则:

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

= - \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= - 2

u = - 2

二次方程组的解是:

u = - 2

u = sec (y)

代回

sec (y) = - 2

sec (y) = - 2

sec (y) = - 2 : y = \frac{2 π}{3} + 2 πn, y = \frac{4 π}{3} + 2 πn

sec (y) = - 2

sec (y) = - 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}

y = \frac{2 π}{3} + 2 πn, y = \frac{4 π}{3} + 2 πn

y = \frac{2 π}{3} + 2 πn, y = \frac{4 π}{3} + 2 πn

合并所有解

y = \frac{2 π}{3} + 2 πn, y = \frac{4 π}{3} + 2 πn

作图

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