Thread: trig help

Find the coordinates of 57pi/3.

but they're not giving me the period, how am i supposed to know?

Originally Posted by NeedHelp18

Find the coordinates of 57pi/3.

Huh? Do you mean the coordinates of the point on the unit circle that corresponds to that angle? Give the problem exactly as it is stated.

Yes, on the unit circle.

Originally Posted by NeedHelp18

Yes, on the unit circle.

The coordinates of any point on the unit circle corresponding to the angle $\displaystyle \theta$ are $\displaystyle (\cos\theta,\,\sin\theta).$

So how do you find the sine and cosine of $\displaystyle \frac{57\pi}3?$ Well, first you should reduce that fraction. Now what is the sine and cosine of any odd multiple of $\displaystyle \pi?$

could i do (54pi/3 + pi)

if so, then what?

Originally Posted by NeedHelp18

could i do (54pi/3 + pi)

What? Is it $\displaystyle \frac{57\pi}3$ or $\displaystyle \frac{54\pi}3?$ In either case, do as I said and simplify the fraction first. What is 54 (or 57) divided by 3?

so it would be 19pi? after i divide it by 3

are the coordinates (1, 0)?

Originally Posted by NeedHelp18

so it would be 19pi? after i divide it by 3

are the coordinates (1, 0)?

Try again with the $\displaystyle x$-coordinate. What is the cosine of an odd multiple of $\displaystyle \pi?$

is it -1?

Originally Posted by NeedHelp18

is it -1?

Yes. The angle $\displaystyle 19\pi$ is coterminal with $\displaystyle \pi,$ and $\displaystyle \cos\pi=-1.$