zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

tan(2x)=(130)/(-270-120)

解答

tan (2 x) = \frac{130}{- 270 - 120}

解答

x = - \frac{0.32175 \dots}{2} + \frac{πn}{2}

+1

弧度

x = - \frac{0.32175 \dots}{2} + \frac{π}{2} n

求解步骤

tan (2 x) = \frac{130}{- 270 - 120}

化简

\frac{130}{- 270 - 120} : - \frac{1}{3}

\frac{130}{- 270 - 120}

数字相减:

- 270 - 120 = - 390

= \frac{130}{- 390}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{130}{390}

约分:

130

= - \frac{1}{3}

使用反三角函数性质

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

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

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

2 x = arctan (- \frac{1}{3}) + πn

2 x = arctan (- \frac{1}{3}) + πn

解

2 x = arctan (- \frac{1}{3}) + πn : x = - \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

2 x = arctan (- \frac{1}{3}) + πn

化简

arctan (- \frac{1}{3}) + πn : - arctan (\frac{1}{3}) + πn

arctan (- \frac{1}{3}) + πn

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{3}) = - arctan (\frac{1}{3})

= - arctan (\frac{1}{3}) + πn

2 x = - arctan (\frac{1}{3}) + πn

两边除以

2

2 x = - arctan (\frac{1}{3}) + πn

两边除以

2

\frac{2 x}{2} = - \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

化简

x = - \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

以小数形式表示解

x = - \frac{0.32175 \dots}{2} + \frac{πn}{2}

作图

流行的例子

-3sin(x)-2cos(2x)=0

- 3 sin (x) - 2 cos (2 x) = 0

2cos(x)tan(x)=1

2 cos (x) tan (x) = 1

sin(10x)=sin(7x)

sin (10 x) = sin (7 x)

185=(220sqrt(2))/pi-cos(pi)+cos(x)

185 = \frac{220 2}{π} - cos (π) + cos (x)

solvefor x,2sin^2(x)=sin(x)

so l v e f or x, 2 sin^{2} (x) = sin (x)