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受欢迎的三角函数 >

cos(2arctan(4/3))

解答

cos (2 arctan (\frac{4}{3}))

解答

- \frac{7}{25}

+1

十进制

- 0.28

求解步骤

cos (2 arctan (\frac{4}{3}))

使用三角恒等式改写:

2 cos^{2} (arctan (\frac{4}{3})) - 1

cos (2 arctan (\frac{4}{3}))

使用倍角公式:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (arctan (\frac{4}{3})) - 1

= 2 cos^{2} (arctan (\frac{4}{3})) - 1

使用三角恒等式改写:

cos (arctan (\frac{4}{3})) = \frac{3}{5}

cos (arctan (\frac{4}{3}))

使用三角恒等式改写:

cos (arctan (\frac{4}{3})) = \frac{1 + ( \frac{4}{3} ) ^{2}}{1 + ( \frac{4}{3} ) ^{2}}

利用以下特性:

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

= \frac{1 + ( \frac{4}{3} ) ^{2}}{1 + ( \frac{4}{3} ) ^{2}}

= \frac{1 + ( \frac{4}{3} ) ^{2}}{1 + ( \frac{4}{3} ) ^{2}}

化简

= \frac{3}{5}

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

化简

2 (\frac{3}{5})^{2} - 1 : - \frac{7}{25}

2 (\frac{3}{5})^{2} - 1

2 (\frac{3}{5})^{2} = \frac{18}{25}

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

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

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

使用指数法则:

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

= \frac{3 ^{2}}{5 ^{2}}

= 2 \cdot \frac{3 ^{2}}{5 ^{2}}

分式相乘:

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

= \frac{3 ^{2} \cdot 2}{5 ^{2}}

3^{2} \cdot 2 = 18

3^{2} \cdot 2

3^{2} = 9

= 9 \cdot 2

数字相乘:

9 \cdot 2 = 18

= 18

= \frac{18}{5 ^{2}}

5^{2} = 25

= \frac{18}{25}

= \frac{18}{25} - 1

将项转换为分式:

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

= - \frac{1 \cdot 25}{25} + \frac{18}{25}

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 25 + 18}{25}

- 1 \cdot 25 + 18 = - 7

- 1 \cdot 25 + 18

数字相乘:

1 \cdot 25 = 25

= - 25 + 18

数字相加/相减:

- 25 + 18 = - 7

= - 7

= \frac{- 7}{25}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{7}{25}

= - \frac{7}{25}

流行的例子

cos^{2} (- 1)

arctan (0.36)

sin (\frac{22 π}{3})

sin^{2} (\frac{π}{8})

sec (\frac{- 5 π}{6})