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受欢迎的三角函数 >

2sec(x)+4=sec(x)+6

解答

2 sec (x) + 4 = sec (x) + 6

解答

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

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

求解步骤

2 sec (x) + 4 = sec (x) + 6

用替代法求解

2 sec (x) + 4 = sec (x) + 6

令

: sec (x) = u

2 u + 4 = u + 6

2 u + 4 = u + 6 : u = 2

2 u + 4 = u + 6

将

4

到右边

2 u + 4 = u + 6

两边减去

4

2 u + 4 - 4 = u + 6 - 4

化简

2 u = u + 2

2 u = u + 2

将

u

para o lado esquerdo

2 u = u + 2

两边减去

u

2 u - u = u + 2 - u

化简

u = 2

u = 2

u = sec (x)

代回

sec (x) = 2

sec (x) = 2

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

合并所有解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

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