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受欢迎的三角函数 >

tan(θ)=(-11/3-(-4/3))/(1+(-4/3)(-11/3))

解答

tan (θ) = \frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

解答

θ = - 0.37724 \dots + πn

求解步骤

tan (θ) = \frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

化简

\frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )} : - \frac{21}{53}

\frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

去除括号:

(- a) = - a, - (- a) = a

= \frac{- \frac{11}{3} + \frac{4}{3}}{1 + \frac{4}{3} \cdot \frac{11}{3}}

\frac{4}{3} \cdot \frac{11}{3} = \frac{44}{9}

\frac{4}{3} \cdot \frac{11}{3}

分式相乘:

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

= \frac{4 \cdot 11}{3 \cdot 3}

数字相乘:

4 \cdot 11 = 44

= \frac{44}{3 \cdot 3}

数字相乘:

3 \cdot 3 = 9

= \frac{44}{9}

= \frac{- \frac{11}{3} + \frac{4}{3}}{1 + \frac{44}{9}}

化简

- \frac{11}{3} + \frac{4}{3} : - \frac{7}{3}

- \frac{11}{3} + \frac{4}{3}

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{- 11 + 4}{3}

数字相加/相减:

- 11 + 4 = - 7

= \frac{- 7}{3}

使用分式法则:

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

= - \frac{7}{3}

= \frac{- \frac{7}{3}}{1 + \frac{44}{9}}

使用分式法则:

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

= - \frac{\frac{7}{3}}{1 + \frac{44}{9}}

使用分式法则:

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

\frac{\frac{7}{3}}{1 + \frac{44}{9}} = \frac{7}{3 ( 1 + \frac{44}{9} )}

= - \frac{7}{3 ( 1 + \frac{44}{9} )}

化简

1 + \frac{44}{9} : \frac{53}{9}

1 + \frac{44}{9}

将项转换为分式:

1 = \frac{1 \cdot 9}{9}

= \frac{1 \cdot 9}{9} + \frac{44}{9}

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 9 + 44}{9}

1 \cdot 9 + 44 = 53

1 \cdot 9 + 44

数字相乘:

1 \cdot 9 = 9

= 9 + 44

数字相加:

9 + 44 = 53

= 53

= \frac{53}{9}

= - \frac{7}{3 \cdot \frac{53}{9}}

乘

3 \cdot \frac{53}{9} : \frac{53}{3}

3 \cdot \frac{53}{9}

分式相乘:

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

= \frac{53 \cdot 3}{9}

数字相乘:

53 \cdot 3 = 159

= \frac{159}{9}

约分:

3

= \frac{53}{3}

= - \frac{7}{\frac{53}{3}}

化简

\frac{7}{\frac{53}{3}} : \frac{21}{53}

\frac{7}{\frac{53}{3}}

使用分式法则:

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

= \frac{7 \cdot 3}{53}

数字相乘:

7 \cdot 3 = 21

= \frac{21}{53}

= - \frac{21}{53}

tan (θ) = - \frac{21}{53}

使用反三角函数性质

tan (θ) = - \frac{21}{53}

tan (θ) = - \frac{21}{53}

的通解

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

θ = arctan (- \frac{21}{53}) + πn

θ = arctan (- \frac{21}{53}) + πn

以小数形式表示解

θ = - 0.37724 \dots + πn

作图

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