Expert: Ahmed Salami - 6/21/2010

Question
find the exact value of sin-1 (-sqrt3/2)
and
cos 5pi/4

Answer
Hi Jose,
a) First, we know that
sin(π/3) = √3/2
but,
sin(π - π/3) = sin(π/3) = √3/2
sin(π + π/3) = -sin(π/3) = -√3/2
sin(2π - π/3) = -sin(π/3) = -√3/2
Therefore,
arcsin(-√3/2) = π + π/3  or  2π - π/3
             = 4π/3  or  5π/3

b) 5π/4 = π + π/4
Now,
cos(π/4) = 1/√2 = √2/2
and so,
cos(π + π/4) = -cos(π/4)
            = -√2/2

Regards