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受欢迎的三角函数 >

cos(arctan(4/3)-arcsin(3/5))

解答

cos (arctan (\frac{4}{3}) - arcsin (\frac{3}{5}))

解答

\frac{24}{25}

+1

十进制

0.96

求解步骤

cos (arctan (\frac{4}{3}) - arcsin (\frac{3}{5}))

使用三角恒等式改写:

cos (arctan (\frac{4}{3})) cos (arcsin (\frac{3}{5})) + sin (arctan (\frac{4}{3})) sin (arcsin (\frac{3}{5}))

cos (arctan (\frac{4}{3}) - arcsin (\frac{3}{5}))

使用角差恒等式:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

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

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

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}

使用三角恒等式改写:

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

cos (arcsin (\frac{3}{5}))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{4}{5}

使用三角恒等式改写:

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

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

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{4}{5}

使用三角恒等式改写:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

利用以下特性:

sin (arcsin (x)) = x

= \frac{3}{5}

= \frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5}

化简

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5} : \frac{24}{25}

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5}

同类项相加:

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5} = 2 \cdot \frac{3}{5} \cdot \frac{4}{5}

= 2 \cdot \frac{3}{5} \cdot \frac{4}{5}

将项转换为分式:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{3}{5} \cdot \frac{4}{5}

分式相乘:

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

= \frac{2 \cdot 3 \cdot 4}{1 \cdot 5 \cdot 5}

数字相乘:

2 \cdot 3 \cdot 4 = 24

= \frac{24}{1 \cdot 5 \cdot 5}

数字相乘:

1 \cdot 5 \cdot 5 = 25

= \frac{24}{25}

= \frac{24}{25}

流行的例子

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

\frac{1}{3} arctan (1)

cot (81 0^{\circ})

- (- cos (0))

arccos (\frac{4}{11})