Cos 3pi
Prove that cos (3pi / 2 + x) = senx? 3
Help function!
cos (3pi / 2 + x) = cos (3pi / 2 + x 2pi) = cos (pi / 2 + x) = senx
Use cosine supplement formula.
cos (a + b) = cos (a) cos (b) sin (a) sin (b)
cos (3pi / 2 + x) = cos (3pi / 2) cos (x) sin (3pi / 2) sin (x)
now
cos (3pi / 2) = 0 and sin (3pi / 2) = 1 again
cos (3pi / 2 + x) = 0 * cos (x) (1) sin (x) = sin (x)
Since cosine is 2pi, cos (theta) = cos (theta 2pi). Then
cos (3pi / 2 + x) = cos (x + 3pi / 2 2pi) = cos (x pi / 2) = sin (x).
