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受欢迎的三角函数 >

sin^2(1/2 arccos(3/5))

解答

sin^{2} (\frac{1}{2} arccos (\frac{3}{5}))

解答

\frac{1}{5}

+1

十进制

0.2

求解步骤

sin^{2} (\frac{1}{2} arccos (\frac{3}{5}))

化简:

\frac{1}{2} arccos (\frac{3}{5}) = \frac{arccos ( \frac{3}{5} )}{2}

\frac{1}{2} arccos (\frac{3}{5})

分式相乘:

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

= \frac{1 \cdot arccos ( \frac{3}{5} )}{2}

乘以:

1 \cdot arccos (\frac{3}{5}) = arccos (\frac{3}{5})

= \frac{arccos ( \frac{3}{5} )}{2}

= sin^{2} (\frac{arccos ( \frac{3}{5} )}{2})

使用三角恒等式改写:

\frac{1 - cos ( arccos ( \frac{3}{5} ) )}{2}

sin^{2} (\frac{arccos ( \frac{3}{5} )}{2})

利用以下特性:

sin^{2} (θ) = \frac{1 - cos ( 2 θ )}{2}

使用倍角公式

cos (2 θ) = 1 - 2 sin^{2} (θ)

交换两边

2 sin^{2} (θ) - 1 = - cos (2 θ)

两边加上

1

2 sin^{2} (θ) = 1 - cos (2 θ)

两边除以

2

sin^{2} (θ) = \frac{1 - cos ( 2 θ )}{2}

= \frac{1 - cos ( 2 \cdot \frac{a r c c o s ( \frac{3}{5} )}{2} )}{2}

化简:

2 \cdot \frac{arccos ( \frac{3}{5} )}{2} = arccos (\frac{3}{5})

2 \cdot \frac{arccos ( \frac{3}{5} )}{2}

分式相乘:

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

= \frac{arccos ( \frac{3}{5} ) \cdot 2}{2}

约分:

2

= arccos (\frac{3}{5})

= \frac{1 - cos ( arccos ( \frac{3}{5} ) )}{2}

= \frac{1 - cos ( arccos ( \frac{3}{5} ) )}{2}

使用三角恒等式改写:

cos (arccos (\frac{3}{5})) = \frac{3}{5}

利用以下特性:

cos (arccos (x)) = x

= \frac{3}{5}

= \frac{1 - \frac{3}{5}}{2}

化简

\frac{1 - \frac{3}{5}}{2} : \frac{1}{5}

\frac{1 - \frac{3}{5}}{2}

化简

1 - \frac{3}{5} : \frac{2}{5}

1 - \frac{3}{5}

将项转换为分式:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} - \frac{3}{5}

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 5 - 3}{5}

1 \cdot 5 - 3 = 2

1 \cdot 5 - 3

数字相乘:

1 \cdot 5 = 5

= 5 - 3

数字相减:

5 - 3 = 2

= 2

= \frac{2}{5}

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

使用分式法则:

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

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

数字相乘:

5 \cdot 2 = 10

= \frac{2}{10}

约分:

2

= \frac{1}{5}

= \frac{1}{5}

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