Math
posted by mysterychicken on .
Use a double or half angle identity to find the exact value of the following expression: if cos x= 4/5 and 270° < x < 360°, find sin 2x
Please help! Thanks

cosx = 4/5 and x is in quad IV
So sinx =  3/5
sin 2x = 2sinxcosx
= 2(3/5)(4/5) = 24/25 
if tan x = 7/24 and 3π/2 < x <2π find cot x/2
Thanks so much! 
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if tanx = 7/24 and x is in IV
then sin x = 7/25 and cosx = 24/25
cot x/2
= cos x/2 / sin x/2
recall cos 2A = 2cos^2 A  1 or 1  2sin^2 A
cos x = 2cos^ x/2  1
24/25 + 1 = 2cos^2 x/2 = 49/25
cos^2 x/2 = 49/50
cos x/2 = 7/(5√2) , if x is in IV , then x/2 is in II , therefore negative
cos x = 1  2sin^2 x/2
24/25  1 = 2sin^2 x/2 = 1/25
sin^2 x/2 = 1/50
sin x/2 = +1/(5√2)
cot x/2 = cos x/2 / sin x/2
= 7/(5√2) / 1/(5√2) = 7 
Thank you soo much!