cos(3A + 180) = sqr(2) / 2?

Answer 1

Cosine of an angle equals postive sqr(2) / 2 when the angle is 45 or 315. (assuming the domain to be [0,360])

So equal angle, which is 3A + 180, to 45 and 315.

3A + 180 = 45
3A + 180 = 315

so the A= 45, and -45

Answer 2

cos(3A + 180) = sqrt(2) / 2; cos(x + y) = cosxcosy - sinxsiny
cos3Acos180 - sin3Asin180 = sqrt(2) / 2; cos180 = -1; sin180 = 0
-cos3A = sqrt(2) / 2
3A = Cos-1 [-sqrt(2) / 2]
3A = 135
A = 45

Answer 3

3A+180 = +-45+k*360
3A= -135 +k360 and A= -45 +k*120.Also 3A=-225+k360 and
A=-75+k120.
If you want solutions 0 A= 75,195,315º,45,165 and 285º