Question

Explain the connection between angles and complex numbers we've been relying on. Illustrate
this by finding the sine and cosine of
1. A 22.5 degree angle, and
2. twice the angle in a 5-12-13 triangle opposite the side of length 5.

Answer 1

let what ever angle you want to find the cosine of be 'x' (in its radian form
and follow the expression cos(x) + i sin(x) = e^(ix)

and expand e^(ix) = 1 + x + (x^2)/2.........

next equate the real and imaginary components