If a and b are two angles in standard position in quadrant i, find cos(a+b) for the given function values. sin a=4/5 and cos b=5/13

First let's find the angles a and b.

 We have then:
 sin a = 4/5
 a = Asin (4/5)
 a = 53.13 degrees.

 cos b = 5/13
 b = Acos5 / 13
 b = 67.38 degrees.

 We now calculate cos (a + b). To do this, we replace the previously found values:
 cos ((53.13) + (67.38)) = - 0.507688738
  
 -0.507688738
 Note: there is another way to solve the problem using trigonometric identities.