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受欢迎的三角函数 >

tan(2arcsin(-5/13))

解答

tan (2 arcsin (- \frac{5}{13}))

解答

- \frac{120}{119}

+1

十进制

- 1.00840 \dots

求解步骤

tan (2 arcsin (- \frac{5}{13}))

使用三角恒等式改写:

- \frac{2 tan ( arcsin ( \frac{5}{13} ) )}{1 - tan ^{2} ( arcsin ( \frac{5}{13} ) )}

tan (2 arcsin (- \frac{5}{13}))

使用倍角公式:

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

= \frac{2 tan ( arcsin ( - \frac{5}{13} ) )}{1 - tan ^{2} ( arcsin ( - \frac{5}{13} ) )}

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{13}) = - arcsin (\frac{5}{13})

= \frac{2 tan ( arcsin ( - \frac{5}{13} ) )}{1 - tan ^{2} ( - arcsin ( \frac{5}{13} ) )}

利用以下特性:

tan (- x) = - tan (x)

tan (- arcsin (\frac{5}{13})) = - tan (arcsin (\frac{5}{13}))

= \frac{2 tan ( arcsin ( - \frac{5}{13} ) )}{1 - ( - tan ( arcsin ( \frac{5}{13} ) ) ) ^{2}}

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{13}) = - arcsin (\frac{5}{13})

= \frac{2 tan ( - arcsin ( \frac{5}{13} ) )}{1 - ( - tan ( arcsin ( \frac{5}{13} ) ) ) ^{2}}

利用以下特性:

tan (- x) = - tan (x)

tan (- arcsin (\frac{5}{13})) = - tan (arcsin (\frac{5}{13}))

= \frac{2 ( - tan ( arcsin ( \frac{5}{13} ) ) )}{1 - ( - tan ( arcsin ( \frac{5}{13} ) ) ) ^{2}}

化简

= - \frac{2 tan ( arcsin ( \frac{5}{13} ) )}{1 - tan ^{2} ( arcsin ( \frac{5}{13} ) )}

= - \frac{2 tan ( arcsin ( \frac{5}{13} ) )}{1 - tan ^{2} ( arcsin ( \frac{5}{13} ) )}

使用三角恒等式改写:

tan (arcsin (\frac{5}{13})) = \frac{5}{12}

tan (arcsin (\frac{5}{13}))

使用三角恒等式改写:

tan (arcsin (\frac{5}{13})) = \frac{( \frac{5}{13} ) 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

利用以下特性:

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

= \frac{( \frac{5}{13} ) 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

= \frac{\frac{5}{13} 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

化简

= \frac{5}{12}

= - \frac{2 \cdot \frac{5}{12}}{1 - ( \frac{5}{12} ) ^{2}}

化简

- \frac{2 \cdot \frac{5}{12}}{1 - ( \frac{5}{12} ) ^{2}} : - \frac{120}{119}

- \frac{2 \cdot \frac{5}{12}}{1 - ( \frac{5}{12} ) ^{2}}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= - \frac{2 \cdot \frac{5}{12}}{- \frac{5 ^{2}}{1 2 ^{2}} + 1}

乘

2 \cdot \frac{5}{12} : \frac{5}{6}

2 \cdot \frac{5}{12}

分式相乘:

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

= \frac{5 \cdot 2}{12}

数字相乘:

5 \cdot 2 = 10

= \frac{10}{12}

约分:

2

= \frac{5}{6}

= - \frac{\frac{5}{6}}{- \frac{5 ^{2}}{1 2 ^{2}} + 1}

\frac{5 ^{2}}{1 2 ^{2}} = \frac{25}{144}

\frac{5 ^{2}}{1 2 ^{2}}

5^{2} = 25

= \frac{25}{1 2 ^{2}}

1 2^{2} = 144

= \frac{25}{144}

= - \frac{\frac{5}{6}}{- \frac{25}{144} + 1}

使用分式法则:

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

= - \frac{5}{6 ( - \frac{25}{144} + 1 )}

化简

1 - \frac{25}{144} : \frac{119}{144}

1 - \frac{25}{144}

将项转换为分式:

1 = \frac{1 \cdot 144}{144}

= \frac{1 \cdot 144}{144} - \frac{25}{144}

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 144 - 25}{144}

1 \cdot 144 - 25 = 119

1 \cdot 144 - 25

数字相乘:

1 \cdot 144 = 144

= 144 - 25

数字相减:

144 - 25 = 119

= 119

= \frac{119}{144}

= - \frac{5}{6 \cdot \frac{119}{144}}

乘

6 \cdot \frac{119}{144} : \frac{119}{24}

6 \cdot \frac{119}{144}

分式相乘:

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

= \frac{119 \cdot 6}{144}

数字相乘:

119 \cdot 6 = 714

= \frac{714}{144}

约分:

6

= \frac{119}{24}

= - \frac{5}{\frac{119}{24}}

化简

\frac{5}{\frac{119}{24}} : \frac{120}{119}

\frac{5}{\frac{119}{24}}

使用分式法则:

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

= \frac{5 \cdot 24}{119}

数字相乘:

5 \cdot 24 = 120

= \frac{120}{119}

= - \frac{120}{119}

= - \frac{120}{119}

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