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受欢迎的三角函数 >

14tan^2(x)=-14tan(x)

解答

14 tan^{2} (x) = - 14 tan (x)

解答

x = πn, x = \frac{3 π}{4} + πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

14 tan^{2} (x) = - 14 tan (x)

用替代法求解

14 tan^{2} (x) = - 14 tan (x)

令

: tan (x) = u

14 u^{2} = - 14 u

14 u^{2} = - 14 u : u = 0, u = - 1

14 u^{2} = - 14 u

将

14 u

para o lado esquerdo

14 u^{2} = - 14 u

两边加上

14 u

14 u^{2} + 14 u = - 14 u + 14 u

化简

14 u^{2} + 14 u = 0

14 u^{2} + 14 u = 0

因式分解

14 u^{2} + 14 u : 14 u (u + 1)

14 u^{2} + 14 u

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 14 uu + 14 u

因式分解出通项

14 u

= 14 u (u + 1)

14 u (u + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or u + 1 = 0

解

u + 1 = 0 : u = - 1

u + 1 = 0

将

1

到右边

u + 1 = 0

两边减去

1

u + 1 - 1 = 0 - 1

化简

u = - 1

u = - 1

二次方程组的解是:

u = 0, u = - 1

u = tan (x)

代回

tan (x) = 0, tan (x) = - 1

tan (x) = 0, tan (x) = - 1

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

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 = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = - 1

tan (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

合并所有解

x = πn, x = \frac{3 π}{4} + πn

作图

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