help with this trig question!?
- Anonymous1 month agoFavorite Answer
x = 2/3.......
- VamanLv 71 month ago
cos x=5/13, sin x= sqrt(13^2-5^2)/13=12/13. Tan x= 12/5
- Anonymous1 month ago
The easiest way to solve this is with the tangent half angle formula (they are really 3 formulas below):
tan(Ѳ/2) = ±√((1 - cos(Ѳ))/(1 + cos(Ѳ))) = sin(Ѳ)/(1-cos(Ѳ)) = csc(Ѳ) - cot(Ѳ)
The first one, ±√((1 - cos(Ѳ))/(1 + cos(Ѳ))), is what you need, since you know
cos(Ѳ) = 5/3.
So just plug it in:
tan(Ѳ/2) = ±√((1 - (5/3))/(1 + (5/3)))
There are 2 potential solutions, a positive and negative one.
There are a lot of trig identities, and it's hard to remember them all. If you can, I recommend looking them up from a table. If you have to memorize them, then memorize the most basic ones first, and try to be able to derive the more complicated ones without needing to memorize them.Source(s): Blessed enough to go to school