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受欢迎的三角函数 >

2-10sec(x)=4-9sec(x)

解答

2 - 10 sec (x) = 4 - 9 sec (x)

解答

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

+1

度数

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

求解步骤

2 - 10 sec (x) = 4 - 9 sec (x)

用替代法求解

2 - 10 sec (x) = 4 - 9 sec (x)

令

: sec (x) = u

2 - 10 u = 4 - 9 u

2 - 10 u = 4 - 9 u : u = - 2

2 - 10 u = 4 - 9 u

将

2

到右边

2 - 10 u = 4 - 9 u

两边减去

2

2 - 10 u - 2 = 4 - 9 u - 2

化简

- 10 u = - 9 u + 2

- 10 u = - 9 u + 2

将

9 u

para o lado esquerdo

- 10 u = - 9 u + 2

两边加上

9 u

- 10 u + 9 u = - 9 u + 2 + 9 u

化简

- u = 2

- u = 2

两边除以

- 1

- u = 2

两边除以

- 1

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

化简

u = - 2

u = - 2

u = sec (x)

代回

sec (x) = - 2

sec (x) = - 2

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

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

合并所有解

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

作图

流行的例子

7=e^{2sin(x)}+3

7 = e^{2 s i n (x)} + 3

sin (u) = - 0.9

-3/2 =-1/2 sec(x)

- \frac{3}{2} = - \frac{1}{2} sec (x)

sin (3 x + 1) = \frac{1}{2}

cos(x)=(13^2+18^2-28^2)/(2*13*18)

cos (x) = \frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}