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受欢迎的三角函数 >

tan(x/2)=-1/(sqrt(3))

解答

tan (\frac{x}{2}) = - \frac{1}{3}

解答

x = \frac{5 π}{3} + 2 πn

求解步骤

tan (\frac{x}{2}) = - \frac{1}{3}

化简

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

乘以共轭根式

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= - \frac{3}{3}

tan (\frac{x}{2}) = - \frac{3}{3}

tan (\frac{x}{2}) = - \frac{3}{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}

\frac{x}{2} = \frac{5 π}{6} + πn

\frac{x}{2} = \frac{5 π}{6} + πn

解

\frac{x}{2} = \frac{5 π}{6} + πn : x = \frac{5 π}{3} + 2 πn

\frac{x}{2} = \frac{5 π}{6} + πn

在两边乘以

2

\frac{x}{2} = \frac{5 π}{6} + πn

在两边乘以

2

\frac{2 x}{2} = 2 \cdot \frac{5 π}{6} + 2 πn

化简

\frac{2 x}{2} = 2 \cdot \frac{5 π}{6} + 2 πn

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

2 \cdot \frac{5 π}{6} + 2 πn : \frac{5 π}{3} + 2 πn

2 \cdot \frac{5 π}{6} + 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π 2}{6}

数字相乘:

5 \cdot 2 = 10

= \frac{10 π}{6}

约分:

2

= \frac{5 π}{3}

= \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

作图

流行的例子

solvefor u,x=2cos(u)cos(v)

so l v e f or u, x = 2 cos (u) cos (v)

cos(θ)=cos(3θ)

cos (θ) = cos (3 θ)

cot(3θ)=sqrt(3)

cot (3 θ) = 3

tan (x) = \frac{45}{35}

(625^{cos^2(x)})/(25^{cos(x))}=1

\frac{62 5 ^{c o s^{2} (x)}}{2 5 ^{c o s (x)}} = 1