arcsin(cos((43pi)/5))

解答

arcsin (cos (\frac{43 π}{5}))

- \frac{π}{10}

十进制

- 18

求解步骤

arcsin (cos (\frac{43 π}{5}))

使用三角恒等式改写:

cos (\frac{43 π}{5}) = sin (- \frac{81 π}{10})

cos (\frac{43 π}{5})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{43 π}{5})

= sin (- \frac{81 π}{10})

= arcsin (sin (- \frac{81 π}{10}))

Use the inverse trig property:

- \frac{π}{10}

arcsin (sin (- \frac{81 π}{10}))

对于

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

使用三角恒等式改写:

sin (- \frac{81 π}{10}) = sin (- \frac{π}{10})

sin (- \frac{81 π}{10})

sin (x + 2 π \cdot k) = sin (x)

= sin (- \frac{81 π}{10} + 4 \cdot 2 π)

= sin (- \frac{π}{10})

= arcsin (sin (- \frac{π}{10}))

- \frac{π}{2} \leq - \frac{π}{10} \leq \frac{π}{2}

= - \frac{π}{10}

= - \frac{π}{10}

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\frac{sin ^{3} ( \frac{π}{2} )}{3}

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