arcsin(sin((5pi)/8))

解答

arcsin (sin (\frac{5 π}{8}))

\frac{3 π}{8}

十进制

67.5

求解步骤

arcsin (sin (\frac{5 π}{8}))

Use the inverse trig property:

\frac{3 π}{8}

arcsin (sin (\frac{5 π}{8}))

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{5 π}{8}) = sin (\frac{3 π}{8})

sin (\frac{5 π}{8})

sin (x) = sin (π - (x))

= sin (π - \frac{5 π}{8})

= sin (\frac{3 π}{8})

= arcsin (sin (\frac{3 π}{8}))

- \frac{π}{2} \leq \frac{3 π}{8} \leq \frac{π}{2}

= \frac{3 π}{8}

= \frac{3 π}{8}

sin (3.14)

\frac{7}{sin ( 3 0 ^{\circ} )}

tan^{2} (\frac{π}{6})

arccot (4)

arccos (tan (- \frac{π}{4}))