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受欢迎的三角函数 >

3sec^2(x)-6=0,0<= x<= 2pi

解答

3 sec^{2} (x) - 6 = 0, 0 \leq x \leq 2 π

解答

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

+1

度数

x = 4 5^{\circ}, x = 31 5^{\circ}, x = 13 5^{\circ}, x = 22 5^{\circ}

求解步骤

3 sec^{2} (x) - 6 = 0, 0 \leq x \leq 2 π

用替代法求解

3 sec^{2} (x) - 6 = 0

令

: sec (x) = u

3 u^{2} - 6 = 0

3 u^{2} - 6 = 0 : u = 2, u = - 2

3 u^{2} - 6 = 0

将

6

到右边

3 u^{2} - 6 = 0

两边加上

6

3 u^{2} - 6 + 6 = 0 + 6

化简

3 u^{2} = 6

3 u^{2} = 6

两边除以

3

3 u^{2} = 6

两边除以

3

\frac{3 u ^{2}}{3} = \frac{6}{3}

化简

u^{2} = 2

u^{2} = 2

对于

x^{2} = f (a)

解为

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

u = 2, u = - 2

u = sec (x)

代回

sec (x) = 2, sec (x) = - 2

sec (x) = 2, sec (x) = - 2

sec (x) = 2, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{7 π}{4}

sec (x) = 2, 0 \leq x \leq 2 π

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}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{4}, x = \frac{7 π}{4}

sec (x) = - 2, 0 \leq x \leq 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

sec (x) = - 2, 0 \leq x \leq 2 π

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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{3 π}{4}, x = \frac{5 π}{4}

合并所有解

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

作图

流行的例子

cot^{2} (x) = 1

2tan(x)-sec^2(x)=0

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

4 sin^{2} (2 x) + 2 = 3

-1/4 sin(x/2)=0

- \frac{1}{4} sin (\frac{x}{2}) = 0

8|sin(pix)-1/4 |+1=7

8 sin (π x) - \frac{1}{4} + 1 = 7