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受欢迎的三角函数 >

sin(2arctan(15/8))

解答

sin (2 arctan (\frac{15}{8}))

解答

\frac{240}{289}

+1

十进制

0.83044 \dots

求解步骤

sin (2 arctan (\frac{15}{8}))

使用三角恒等式改写:

2 sin (arctan (\frac{15}{8})) cos (arctan (\frac{15}{8}))

sin (2 arctan (\frac{15}{8}))

使用倍角公式:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (arctan (\frac{15}{8})) cos (arctan (\frac{15}{8}))

= 2 sin (arctan (\frac{15}{8})) cos (arctan (\frac{15}{8}))

使用三角恒等式改写:

sin (arctan (\frac{15}{8})) = \frac{15}{17}

sin (arctan (\frac{15}{8}))

使用三角恒等式改写:

sin (arctan (\frac{15}{8})) = \frac{( \frac{15}{8} ) 1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

利用以下特性:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{15}{8} ) 1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

= \frac{\frac{15}{8} 1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

化简

= \frac{15}{17}

使用三角恒等式改写:

cos (arctan (\frac{15}{8})) = \frac{8}{17}

cos (arctan (\frac{15}{8}))

使用三角恒等式改写:

cos (arctan (\frac{15}{8})) = \frac{1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

利用以下特性:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

= \frac{1 + ( \frac{15}{8} ) ^{2}}{1 + ( \frac{15}{8} ) ^{2}}

化简

= \frac{8}{17}

= 2 \cdot \frac{15}{17} \cdot \frac{8}{17}

化简

2 \cdot \frac{15}{17} \cdot \frac{8}{17} : \frac{240}{289}

2 \cdot \frac{15}{17} \cdot \frac{8}{17}

将项转换为分式:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{8}{17} \cdot \frac{15}{17}

分式相乘:

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

= \frac{2 \cdot 15 \cdot 8}{1 \cdot 17 \cdot 17}

数字相乘:

2 \cdot 15 \cdot 8 = 240

= \frac{240}{1 \cdot 17 \cdot 17}

数字相乘:

1 \cdot 17 \cdot 17 = 289

= \frac{240}{289}

= \frac{240}{289}

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