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受欢迎的三角函数 >

5sec^2(x)-5=0

解答

5 sec^{2} (x) - 5 = 0

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

5 sec^{2} (x) - 5 = 0

用替代法求解

5 sec^{2} (x) - 5 = 0

令

: sec (x) = u

5 u^{2} - 5 = 0

5 u^{2} - 5 = 0 : u = 1, u = - 1

5 u^{2} - 5 = 0

将

5

到右边

5 u^{2} - 5 = 0

两边加上

5

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

化简

5 u^{2} = 5

5 u^{2} = 5

两边除以

5

5 u^{2} = 5

两边除以

5

\frac{5 u ^{2}}{5} = \frac{5}{5}

化简

u^{2} = 1

u^{2} = 1

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

使用法则

1 = 1

= 1

- 1 = - 1

- 1

使用法则

1 = 1

= - 1

u = 1, u = - 1

u = sec (x)

代回

sec (x) = 1, sec (x) = - 1

sec (x) = 1, sec (x) = - 1

sec (x) = 1 : x = 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 = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 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 = 2 πn, x = π + 2 πn

作图

流行的例子

cos (3 θ) = - \frac{1}{2}

cos (x) = \frac{5}{6}

1 - tan^{2} (x) = 0

cos(x)cos(3x)-sin(x)sin(3x)=0

cos (x) cos (3 x) - sin (x) sin (3 x) = 0

(cot(θ)-1)(sin(θ)-1)=0

(cot (θ) - 1) (sin (θ) - 1) = 0