Cos 3 alpha = - 0.1 solutions in degree

Answer 1

what's the problem?

cos 3θ = -0.1
3θ = cos<su>-1(-.1)
3θ = 95.74°
θ = 31.91°

sorry about the θ -- didn't have an alpha handy.

Answer 2

oops
cos 3θ = -0.1
3θ = cos^-1-.1
3θ = 95.74°
θ = 31.91°

Answer 3

you know the cosine is negative in II and III
cos 84.26° = +.1
so 3 alpha = 180 -84.26 or 3alpha = 180+84.26
alpha = 31.9° or 88.1°

You did not state the domain of alpha, I will assume between 0 and 360°
period of cos 3alpha is 360°/3 = 120°
so adding 120 to any answer will yield a new answer
alpha = 31.9 +120 = 151.9
alpha = 151.9+10 = 271.9
alpha = 271.9+120 = 391.9 -- too big

alph = 88.1+120 = 208.1
alpha = 208.1+120 = 328.1

alpha = 31.9, 88.1, 151.9, 208.1, 271.9, and 328.1