Given that tangent theta equals three halves comma pi less than theta less than startfraction 3 pi over 2 endfraction commatanθ=32, π< θ< 3π2,
find the exact value of each of the following.

(a) sine left parenthesis 2 theta right parenthesissin(2θ)
(b) cosine left parenthesis 2 theta right parenthesiscos(2θ)
(c) sine startfraction theta over 2 endfractionsinθ2
(d) cosine startfraction theta over 2 endfractioncosθ2
(e) tangent left parenthesis 2 theta right parenthesistan(2θ)
(f) tangent startfraction theta over 2 endfractiontanθ2(a)  

sine left parenthesis 2 theta right parenthesissin(2θ)equals=nothing
(type an exact answer, using radicals as needed.)

(b)  cosine left parenthesis 2 theta right parenthesiscos(2θ)equals=nothing
(type an exact answer, using radicals as needed.)  

(c)  sine startfraction theta over 2 endfractionsinθ2equals=nothing
(type an exact answer, using radicals as needed.)

(d)  cosine startfraction theta over 2 endfractioncosθ2equals=nothing

(type an exact answer, using radicals as needed.)

(e) tangent left parenthesis 2 theta right parenthesistan(2θ)equals=nothing

(type an exact answer, using radicals as needed.)

(f) tangent startfraction theta over 2 endfractiontanθ2equals=nothing
(type an exact answer, using radicals as needed.)