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受欢迎的三角函数 >

tan(t)= 3/(tan(t))

解答

tan (t) = \frac{3}{tan ( t )}

解答

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

+1

度数

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

求解步骤

tan (t) = \frac{3}{tan ( t )}

用替代法求解

tan (t) = \frac{3}{tan ( t )}

令

: tan (t) = u

u = \frac{3}{u}

u = \frac{3}{u} : u = 3, u = - 3

u = \frac{3}{u}

在两边乘以

u

u = \frac{3}{u}

在两边乘以

u

uu = \frac{3}{u} u

化简

uu : u^{2}

uu = \frac{3}{u} u

使用指数法则:

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

uu = u^{1 + 1}

= u^{1 + 1}

数字相加:

1 + 1 = 2

= u^{2}

u^{2} = 3

u^{2} = 3

解

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

u^{2} = 3

对于

x^{2} = f (a)

解为

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

u = 3, u = - 3

u = 3, u = - 3

验证解

找到无定义的点（奇点）:

u = 0

取

\frac{3}{u}

的分母，令其等于零

u = 0

以下点无定义

u = 0

将不在定义域的点与解相综合:

u = 3, u = - 3

u = tan (t)

代回

tan (t) = 3, tan (t) = - 3

tan (t) = 3, tan (t) = - 3

tan (t) = 3 : t = \frac{π}{3} + πn

tan (t) = 3

tan (t) = 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}

t = \frac{π}{3} + πn

t = \frac{π}{3} + πn

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

tan (t) = - 3

tan (t) = - 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}

t = \frac{2 π}{3} + πn

t = \frac{2 π}{3} + πn

合并所有解

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

作图

流行的例子

tan(-x)=tan(2x+1)

tan (- x) = tan (2 x + 1)

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

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

sin(6x)cos(9x)-cos(6x)sin(9x)=-0.4

sin (6 x) cos (9 x) - cos (6 x) sin (9 x) = - 0.4

sin^2(x)=2tan^2(x)

sin^{2} (x) = 2 tan^{2} (x)

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

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