we will use the formula for the dot product, i hope you know what the dot product is:

we have:

cos(x) = a*b/(|a||b|)

where * means dot product and x is the angle between the two (nonzero) vectors:

a*b = <4,-3>*<4,3> = 4*4 + (-3)*3 = 16 - 9 = 7

|a| = sqrt(4^2 + (-3)^2) = sqrt(25) = 5

|b| = sqrt(4^2 + 3^2) = sqrt(25) = 5

=> cos(x) = 7/(5)(5) = 7/25

=> x = cos^-1(7/25)

=> x = 1.287 radians

or x = 73.74 degrees