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受欢迎的三角函数 >

arctan(0.5)-arctan(1/3)=arctan(x)

解答

arctan (0.5) - arctan (\frac{1}{3}) = arctan (x)

解答

x = \frac{1}{7}

求解步骤

arctan (0.5) - arctan (\frac{1}{3}) = arctan (x)

arctan (0.5) = arctan (\frac{1}{2})

arctan (0.5)

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

交换两边

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

使用反三角函数性质

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

arctan (x) = a \Rightarrow x = tan (a)

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

tan (arctan (\frac{1}{2}) - arctan (\frac{1}{3})) = \frac{1}{7}

tan (arctan (\frac{1}{2}) - arctan (\frac{1}{3}))

使用三角恒等式改写:

\frac{tan ( arctan ( \frac{1}{2} ) ) - tan ( arctan ( \frac{1}{3} ) )}{1 + tan ( arctan ( \frac{1}{2} ) ) tan ( arctan ( \frac{1}{3} ) )}

tan (arctan (\frac{1}{2}) - arctan (\frac{1}{3}))

使用角差恒等式:

tan (s - t) = \frac{tan ( s ) - tan ( t )}{1 + tan ( s ) tan ( t )}

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

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

使用三角恒等式改写:

tan (arctan (\frac{1}{2})) = \frac{1}{2}

利用以下特性:

tan (arctan (x)) = x

= \frac{1}{2}

使用三角恒等式改写:

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

利用以下特性:

tan (arctan (x)) = x

= \frac{1}{3}

= \frac{\frac{1}{2} - \frac{1}{3}}{1 + \frac{1}{2} \cdot \frac{1}{3}}

化简

\frac{\frac{1}{2} - \frac{1}{3}}{1 + \frac{1}{2} \cdot \frac{1}{3}} : \frac{1}{7}

\frac{\frac{1}{2} - \frac{1}{3}}{1 + \frac{1}{2} \cdot \frac{1}{3}}

\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}

\frac{1}{2} \cdot \frac{1}{3}

分式相乘:

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

= \frac{1 \cdot 1}{2 \cdot 3}

数字相乘:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{1}{6}

= \frac{\frac{1}{2} - \frac{1}{3}}{1 + \frac{1}{6}}

化简

\frac{1}{2} - \frac{1}{3} : \frac{1}{6}

\frac{1}{2} - \frac{1}{3}

2, 3

的最小公倍数:

6

2, 3

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

2

或

3

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

6

对于

\frac{1}{2} :

将分母和分子乘以

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

对于

\frac{1}{3} :

将分母和分子乘以

2

\frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}

= \frac{3}{6} - \frac{2}{6}

因为分母相等，所以合并分式:

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

= \frac{3 - 2}{6}

数字相减:

3 - 2 = 1

= \frac{1}{6}

= \frac{\frac{1}{6}}{1 + \frac{1}{6}}

使用分式法则:

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

= \frac{1}{6 ( 1 + \frac{1}{6} )}

化简

1 + \frac{1}{6} : \frac{7}{6}

1 + \frac{1}{6}

将项转换为分式:

1 = \frac{1 \cdot 6}{6}

= \frac{1 \cdot 6}{6} + \frac{1}{6}

因为分母相等，所以合并分式:

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

= \frac{1 \cdot 6 + 1}{6}

1 \cdot 6 + 1 = 7

1 \cdot 6 + 1

数字相乘:

1 \cdot 6 = 6

= 6 + 1

数字相加:

6 + 1 = 7

= 7

= \frac{7}{6}

= \frac{1}{6 \cdot \frac{7}{6}}

乘

6 \cdot \frac{7}{6} : 7

6 \cdot \frac{7}{6}

分式相乘:

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

= \frac{7 \cdot 6}{6}

约分:

6

= 7

= \frac{1}{7}

= \frac{1}{7}

x = \frac{1}{7}

x = \frac{1}{7}

作图

流行的例子

arctan (x) = 3 0^{\circ}

solvefor x,(cos(x))/(tag)= 3/2

so l v e f or x, \frac{cos ( x )}{t a g} = \frac{3}{2}

sin^3(x)=2sin(x)

sin^{3} (x) = 2 sin (x)

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

2sin(3x)=1,0<= x<= 2pi

2 sin (3 x) = 1, 0 \leq x \leq 2 π