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

Answer:

-0.507688738

Note: there is another way to solve the problem using trigonometric identities.