Question

Let sin ? = 4/5, and cos ? = ?3/5, and find the indicated value

Answer 1

Let the unknown angle be x.
That is
sin x = 4/5
cos x = 3/5

By drawing a right triangle in the first quadrant,
hypotenuse = 5
Adjacent side = 3
opposite side = 4

That is tan x  = 4/3
From the calculator,
x = arctan(4/3) = 53 deg (nearest integer)

Answer: 53 deg. (nearest integer)