Question

Find the rectangular coordinates of (2/3, -2pi/3)

So far, I have gotten x=1/3 and y=√3/3 but I do not know if either would be negative because 2pi/3 is in the 2nd quadrant so it would usually be negative, but the negative sign (-) is already in front of it so would it just cancel out? I do not know. Can you help me?

Answer 1

I got
\[
\left\{-\frac{1}{3},-\frac{1}{\sqrt{3
}}\right\}
\]
Do you need explanation?

Answer 2

\[
x= \rho \cos(\theta)\\
y= \rho \sin (\theta)\\

\]

Answer 3

\[
\rho= \frac 2 3\\
\theta=- \frac { 2 \pi}3

\]

Answer 4

I know all that. So if there is a negative sign in front of a radian that is in quadrant 2, (like 2pi/3 is) then nothing happens because the negative sign is already present?
or do the 2 negatives cancel out?

Answer 5

\[
\cos( -\frac {2 \pi} 3)=\cos(\frac {2 \pi} 3)=-\frac 1 2\\
\sin( -\frac {2 \pi} 3)=-\sin(\frac {2 \pi} 3)=-\frac{\sqrt{3}}{2}\\

\]

Answer 6

You do not have to worry about signs, just compute correctly the sin and cos as I did above.

Answer 7

How is your background in Trigonometry?

Answer 8

This is my second semester in Pre Calculus 2 (and this semester is just trig) but I am on the last unit and actually, the assignment now before the final.

Answer 9

Did you understand how I computed the sin and the cos above?

Answer 10

Yes I did. But what I was asking never clarified in the course. And I am in an online class so I have no teacher to ask.

Answer 11

You have a teacher right now.

Answer 12

Go to my online test and practice some trig and calc questions:
http://mathonline.missouri.edu

Answer 13

Ok! And thank you so much for the help :)