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受欢迎的三角函数 >

4tan^2(x)-12=0

解答

4 tan^{2} (x) - 12 = 0

解答

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

+1

度数

x = 6 0^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 18 0^{\circ} n

求解步骤

4 tan^{2} (x) - 12 = 0

用替代法求解

4 tan^{2} (x) - 12 = 0

令

: tan (x) = u

4 u^{2} - 12 = 0

4 u^{2} - 12 = 0 : u = 3, u = - 3

4 u^{2} - 12 = 0

将

12

到右边

4 u^{2} - 12 = 0

两边加上

12

4 u^{2} - 12 + 12 = 0 + 12

化简

4 u^{2} = 12

4 u^{2} = 12

两边除以

4

4 u^{2} = 12

两边除以

4

\frac{4 u ^{2}}{4} = \frac{12}{4}

化简

u^{2} = 3

u^{2} = 3

对于

x^{2} = f (a)

解为

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

u = 3, u = - 3

u = tan (x)

代回

tan (x) = 3, tan (x) = - 3

tan (x) = 3, tan (x) = - 3

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 3

tan (x) = 3

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = - 3

tan (x) = - 3

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

合并所有解

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

作图

流行的例子

tan(θ)-1/(sqrt(3))=0

tan (θ) - \frac{1}{3} = 0

tan(x/2+pi/3)=1

tan (\frac{x}{2} + \frac{π}{3}) = 1

-cot(x)+csc(x)=1

- cot (x) + csc (x) = 1

cot (\frac{x}{2}) = 0

sin^2(θ)=2sin(θ)+3

sin^{2} (θ) = 2 sin (θ) + 3