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.)

Read the excerpt from the strange case of dr jekyll and mr. hyde what do dr. jekyll's thoughts reveal about him in this excerpt? [t]he inmates of my house were locked in the most rigorous hours of slumber, and i determined, flushed as i was with hope and triumph, to venture in my new shape as far as to my bedroom. i crossed the yard, wherein the constellations looked down upon me, i could have thought, with wonder, the first creature of that sort that their unsleeping vigilance had yet disclosed to he is jealous of those who can sleep through the night. he is revered for his scientific advances. he is interested in studying the movements of the stars he is proud and enthusiastic about his initial results.