Determine the value of cos(theta) given that cos(pi − theta) = .2

(A)p.96 (B) .2 (C) −.2 (D) −sqrt.96 (E) None of the above.

One of the basic properties is

cos(π-Ø) = -cosØ , based on the CAST rule
so you have
cosØ = - .2

you can also get it using
cos(π-Ø)
= cosπcosØ + sinπcosØ
= (-1)cos∏ + (0)cosØ
= - cosØ