Question

Using double angle identities:
Find sin (2x). if tan x =12/5 and pi < x < 3pi/2

Answer 1

tan x = opp/adj. Since they're in pi <x< 3pi/2, they are both negative. So:
opp= -12
adj = -5
Use (-12)^2 + (-5)^2 = c^2 .
hypotenuse = c= 13 , hyp has no negative sign.

sin u = 2sin u cos u
sin (2x) = 2 (-12/13) (-5/13)
= 120/169 = 0.7101

Answer 2

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