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受欢迎的三角函数 >

5tan^2(x)-15=0

解答

5 tan^{2} (x) - 15 = 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

5 tan^{2} (x) - 15 = 0

用替代法求解

5 tan^{2} (x) - 15 = 0

令

: tan (x) = u

5 u^{2} - 15 = 0

5 u^{2} - 15 = 0 : u = 3, u = - 3

5 u^{2} - 15 = 0

将

15

到右边

5 u^{2} - 15 = 0

两边加上

15

5 u^{2} - 15 + 15 = 0 + 15

化简

5 u^{2} = 15

5 u^{2} = 15

两边除以

5

5 u^{2} = 15

两边除以

5

\frac{5 u ^{2}}{5} = \frac{15}{5}

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

-2cos^2(x)=-cos(x)-1

- 2 cos^{2} (x) = - cos (x) - 1

sin (θ) = - \frac{2}{5}

-sin^2(x)=2cos(x)-2

- sin^{2} (x) = 2 cos (x) - 2

3sin(2θ)-5sin(θ)=0

3 sin (2 θ) - 5 sin (θ) = 0

cos(2x)=cos(x),0<= x<= 2pi

cos (2 x) = cos (x), 0 \leq x \leq 2 π