range of

Question

sin(siny) +cos(siny)

Answer 1

sin y can take on values between -1 and 1.

For any value of siny between -1 and 1, the range of
sin(siny) + cosine(siny) is between
-sqrt2 and +sqrt2.
Extreme values of sin(siny) + cos(siny) occur where sin(siny) = cos(siny)
siny = +or- (sqrt2)/2