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受欢迎的三角函数 >

5sec^2(x)-5=0,0<= x<2pi

解答

5 sec^{2} (x) - 5 = 0, 0 \leq x < 2 π

解答

x = 0, x = π

+1

度数

x = 0^{\circ}, x = 18 0^{\circ}

求解步骤

5 sec^{2} (x) - 5 = 0, 0 \leq x < 2 π

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, 0 \leq x < 2 π : x = 0

sec (x) = 1, 0 \leq x < 2 π

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

在

0 \leq x < 2 π

范围内的解

x = 0

sec (x) = - 1, 0 \leq x < 2 π : x = π

sec (x) = - 1, 0 \leq x < 2 π

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

在

0 \leq x < 2 π

范围内的解

x = π

合并所有解

x = 0, x = π

作图

流行的例子

2 sin (5 x) + 3 = 2

5sin(y)-5=3sin(y)-4

5 sin (y) - 5 = 3 sin (y) - 4

2cos^2(x)+3cos(x)-3=0

2 cos^{2} (x) + 3 cos (x) - 3 = 0

3sin(x)-5cos(x)=0

3 sin (x) - 5 cos (x) = 0

sin^{2} (x) = 0.85