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受欢迎的三角函数 >

sin(2arctan(1/2))

解答

sin (2 arctan (\frac{1}{2}))

解答

\frac{4}{5}

+1

十进制

0.8

求解步骤

sin (2 arctan (\frac{1}{2}))

使用三角恒等式改写:

2 sin (arctan (\frac{1}{2})) cos (arctan (\frac{1}{2}))

sin (2 arctan (\frac{1}{2}))

使用倍角公式:

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

= 2 sin (arctan (\frac{1}{2})) cos (arctan (\frac{1}{2}))

= 2 sin (arctan (\frac{1}{2})) cos (arctan (\frac{1}{2}))

使用三角恒等式改写:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

sin (arctan (\frac{1}{2}))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{5}{5}

使用三角恒等式改写:

cos (arctan (\frac{1}{2})) = \frac{2 5}{5}

cos (arctan (\frac{1}{2}))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{2 5}{5}

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

化简

2 \cdot \frac{5}{5} \cdot \frac{2 5}{5} : \frac{4}{5}

2 \cdot \frac{5}{5} \cdot \frac{2 5}{5}

分式相乘:

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

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

5 \cdot 25 \cdot 2 = 20

5 \cdot 25 \cdot 2

数字相乘:

2 \cdot 2 = 4

= 455

使用根式运算法则:

a a = a

55 = 5

= 4 \cdot 5

数字相乘:

4 \cdot 5 = 20

= 20

= \frac{20}{5 \cdot 5}

数字相乘:

5 \cdot 5 = 25

= \frac{20}{25}

约分:

5

= \frac{4}{5}

= \frac{4}{5}

流行的例子

arccos (\frac{9}{17})

arcsin (\frac{7}{4})

tan(arcsin(15/17))

tan (arcsin (\frac{15}{17}))

arccos (- \frac{5}{7})

arcsin (0.766)