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受欢迎的三角函数 >

cos^2(1/2 arccos(12/13))

解答

cos^{2} (\frac{1}{2} arccos (\frac{12}{13}))

解答

\frac{25}{26}

+1

十进制

0.96153 \dots

求解步骤

cos^{2} (\frac{1}{2} arccos (\frac{12}{13}))

化简:

\frac{1}{2} arccos (\frac{12}{13}) = \frac{arccos ( \frac{12}{13} )}{2}

\frac{1}{2} arccos (\frac{12}{13})

分式相乘:

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

= \frac{1 \cdot arccos ( \frac{12}{13} )}{2}

乘以:

1 \cdot arccos (\frac{12}{13}) = arccos (\frac{12}{13})

= \frac{arccos ( \frac{12}{13} )}{2}

= cos^{2} (\frac{arccos ( \frac{12}{13} )}{2})

使用三角恒等式改写:

\frac{1 + cos ( arccos ( \frac{12}{13} ) )}{2}

cos^{2} (\frac{arccos ( \frac{12}{13} )}{2})

利用以下特性:

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

使用倍角公式

cos (2 θ) = 2 cos^{2} (θ) - 1

交换两边

2 cos^{2} (θ) - 1 = cos (2 θ)

两边加上

1

2 sin^{2} (θ) = 1 + cos (2 θ)

两边除以

2

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

= \frac{1 + cos ( 2 \cdot \frac{a r c c o s ( \frac{12}{13} )}{2} )}{2}

化简:

2 \cdot \frac{arccos ( \frac{12}{13} )}{2} = arccos (\frac{12}{13})

2 \cdot \frac{arccos ( \frac{12}{13} )}{2}

分式相乘:

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

= \frac{arccos ( \frac{12}{13} ) \cdot 2}{2}

约分:

2

= arccos (\frac{12}{13})

= \frac{1 + cos ( arccos ( \frac{12}{13} ) )}{2}

= \frac{1 + cos ( arccos ( \frac{12}{13} ) )}{2}

使用三角恒等式改写:

cos (arccos (\frac{12}{13})) = \frac{12}{13}

利用以下特性:

cos (arccos (x)) = x

= \frac{12}{13}

= \frac{1 + \frac{12}{13}}{2}

化简

\frac{1 + \frac{12}{13}}{2} : \frac{25}{26}

\frac{1 + \frac{12}{13}}{2}

化简

1 + \frac{12}{13} : \frac{25}{13}

1 + \frac{12}{13}

将项转换为分式:

1 = \frac{1 \cdot 13}{13}

= \frac{1 \cdot 13}{13} + \frac{12}{13}

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 13 + 12}{13}

1 \cdot 13 + 12 = 25

1 \cdot 13 + 12

数字相乘:

1 \cdot 13 = 13

= 13 + 12

数字相加:

13 + 12 = 25

= 25

= \frac{25}{13}

= \frac{\frac{25}{13}}{2}

使用分式法则:

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

= \frac{25}{13 \cdot 2}

数字相乘:

13 \cdot 2 = 26

= \frac{25}{26}

= \frac{25}{26}

流行的例子

3 sin (9 0^{\circ})

cos(arcsin(-4/5))

cos (arcsin (- \frac{4}{5}))

2 \cdot sin (6 0^{\circ})

6 sin (0)

sinh (ln (3))