arccos(cos((8pi)/5))

解答

arccos (cos (\frac{8 π}{5}))

\frac{2 π}{5}

十进制

72

求解步骤

arccos (cos (\frac{8 π}{5}))

Use the inverse trig property:

\frac{2 π}{5}

arccos (cos (\frac{8 π}{5}))

对于

0 \leq x \leq π, a rccos (cos (x)) = x

使用三角恒等式改写:

cos (\frac{8 π}{5}) = cos (\frac{2 π}{5})

cos (\frac{8 π}{5})

cos (x) = cos (2 π - (x))

= cos (2 π - \frac{8 π}{5})

= cos (\frac{2 π}{5})

= arccos (cos (\frac{2 π}{5}))

0 \leq \frac{2 π}{5} \leq π

= \frac{2 π}{5}

= \frac{2 π}{5}

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