Expert: Sherman D. - 3/9/2008

Question
Dear Sherman,

For some reason I have been put in an advanced mathematics class at my school.  I do farely well averaging a 90 average, but i would like to do better.  We are currently studying Trigonometry.  I don't really understand it.  I was given a worksheet with 16 questions, I got to number 11 and stopped because I have NO IDEA what to do first, second, or last.  Can you help me?

if (theta) is an angle in standard position and its terminal side passes through point (-1/2, sq.rt.3/2) on a unit circle, then a possible value of (theta) is:
(1)120  (2)150   (3)210   (4)240

If you could show me how to solve this as well as any other tips you may have, I would GREATLY appreciate it!

Thanks in advance,
Eryne

Answer
actually i'm pretty good at trig.

this site should help, http://id.mind.net/~zona/mmts/trigonometryRealms/TrigFuncPointDef/TrigFuncPointD...

sin(A) = y/r
cos(A) = x/r
tan(A) = y/x

tan(A) = (sqrt(3)/2)/(-1/2)
tan(A) = -sqrt(3)
A = pi/3 (60°), 2pi/3 (120°)

keeping this on the -sqrt(3) side

for the angle to pass through point (-1/2, sqrt(3)/2), it would have to be larger than angle A

ANS : 150°

even if you weren't making it -sqrt(3) and you were making it sqrt(3), 120° and 240° doesn't pass through the point because it is the point, and 210° is to small to pass through the point.

Just keep in mind

tan(A) = -n, (x,-y) or (-x,y)
tan(A) = n, (x,y) or (-x,-y)