Question

find the exact value of the trig function
tan 345 degrees

Answer 1

doesn't anyone own a calculator anymore?

Answer 2

i got it down to \[-1+ \sqrt{3}/3/ 1- \sqrt{3}/3\] (if that's right...) but i'm not sure what to do from there

Answer 3

i think you are supposed to use the half angle formula for tangent

Answer 4

let me see if your answer is right, hold on a sec

Answer 5

no, i think you got \(-1\)

Answer 6

so what am i supposed to do with finding the exact value?

Answer 7

what you need to use is this:\[\tan(\frac{x}{2})=\frac{\sin(x)}{1+\cos(x)}\]

Answer 8

345 is half of 690

Answer 9

and 690 is coterminal with 330 or -30 whichever you prefer

Answer 10

i prefer \(-30\) but you can use either
so you get
\[\tan(345)=\frac{\sin(-30)}{1+\cos(-30)}\] as a start

Answer 11

you good from there or you need more help?

Answer 12

oh ok so for the half angle part, you would have to find what divided by 2 will give you the angle that's given?

Answer 13

yeah, i pretty much just made a guess
since 345 is not an angle that you know the sine or cosine or tangent of, i guessed doubling it to see if that was a common one

Answer 14

then since 690 is the coterminal with -30, i knew that was the right thing to do, use the half angle formula

Answer 15

alright, so how would you know when to use the half or double angle formula?