Question #0bee5

1 Answer
May 16, 2016

Answer:

#sin(tan^-1 (3/4)+cos^-1 (5/13)) = (3/5)(5/13)+(4/5)(12/13) = 63/65#

Explanation:

#tan^-1(3/4)# is a #theta# between #-pi/2# and #pi/2# with #tan theta = 3/4#

#cos^-1(5/13)# is a #phi# between #0# and #pi# with #cos phi = 5/13#

We have been asked to find #sin(theta + phi)#.

We know that #sin(theta + phi) = sin theta cos phi + cos theta sin phi#

We know that #tan theta = 3/4# and #0 < theta < pi/2#, we can find that #sin theta = 3/5# and #cos theta = 4/5#

We know that #cos phi = 5/13# and #0 < phi < pi/2# so we find #sin phi = 12/13#.

Therefore

#sin(tan^-1 (3/4)+cos^-1 (5/13)) = (3/5)(5/13)+(4/5)(12/13) = 63/65# .