arcsin(sin((3pi)/4))

解答

arcsin (sin (\frac{3 π}{4}))

\frac{π}{4}

十进制

45

求解步骤

arcsin (sin (\frac{3 π}{4}))

Use the inverse trig property:

\frac{π}{4}

arcsin (sin (\frac{3 π}{4}))

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{3 π}{4}) = sin (\frac{π}{4})

sin (\frac{3 π}{4})

sin (x) = sin (π - (x))

= sin (π - \frac{3 π}{4})

= sin (\frac{π}{4})

= arcsin (sin (\frac{π}{4}))

- \frac{π}{2} \leq \frac{π}{4} \leq \frac{π}{2}

= \frac{π}{4}

= \frac{π}{4}

p ro v e sin (2 θ) = 2 sin (θ) cos (θ)

sin (2 x) + sin (x) = 0

p ro v e sec^{2} (x) - tan^{2} (x) = 1

arcsin (sin (\frac{5 π}{4}))

sin^{2} (π)