arcsin(sin((10pi)/7))

解答

arcsin (sin (\frac{10 π}{7}))

- \frac{3 π}{7}

十进制

- 77.14

求解步骤

arcsin (sin (\frac{10 π}{7}))

Use the inverse trig property:

- \frac{3 π}{7}

arcsin (sin (\frac{10 π}{7}))

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{10 π}{7}) = sin (- \frac{3 π}{7})

sin (\frac{10 π}{7})

sin (x) = sin (π - (x))

= sin (π - \frac{10 π}{7})

= sin (- \frac{3 π}{7})

= arcsin (sin (- \frac{3 π}{7}))

- \frac{π}{2} \leq - \frac{3 π}{7} \leq \frac{π}{2}

= - \frac{3 π}{7}

= - \frac{3 π}{7}

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