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Answer 1 · 2017-07-11T16:34:51

#1.357#, in radians.

The other answer assumes that the angles are in degrees. If you're using radians, the correct solution is as follows:

#sin(1/2) = 0.4794#

#cos(1/2) = 0.8776#

#therefore sin(1/2)+cos(1/2) = 1.357#

Answer 2 · 2017-07-12T10:29:08

If you are looking for an equivalent exact expression, not an approximation, use #sina+cosa = sqrt2sin(a+pi/4)#

#sin(1/2)+cos(1/2)#

Observe that #sqrt2cos(pi/4) = 1# and #sqrt2sin(pi/4) = 1#, so

#sin(1/2)+cos(1/2) = sqrt2cos(pi/4) sin(1/2)+sqrt2sin(pi/4) cos(1/2)#

# = sqrt2(sin(1/2)cos(pi/4) + cos(1/2)sin(pi/4))#

# = sqrt2sin(1/2+pi/4)#