Question

what are the coordinates of the terminal point corresponding to θ=10pi/3

Answer 1

without a radius to go by .... it could be any number of points on a line

Answer 2

thats the only information they gave me

Answer 3

you cant define a point with just an angle ....

Answer 4

Probably assuming the unit circle, I would guess, in which case the radius would be 1.

Answer 5

thanks, so what would the terminal point be?

Answer 6

Well, if we have \( r = 1\) and \(\theta = 10\pi/3\) I believe that means \[x = r\cos\theta\ = 1\cos 10\pi/3 = \cos 4\pi/3 = -\frac{1}{2}\] and \[y=r\sin\theta\ = 1\sin 10\pi/3 = \sin 4\pi/3 = -\frac{\sqrt{3}}{2}\]

Answer 7

oh ok i see, ill go over that again to be sure i understand. thanks so much :)
is -√3/2 the terminal point?

Answer 8

No, \((-\dfrac{1}{2},-\dfrac{\sqrt{3}}{2})\) would be the terminal point.

Answer 9

ohhh that makes much more sense now. i was reading it all as one. so you found the first point and then found the second. i see

Answer 10

I used the principle that adding or subtracting \(2\pi\) to the argument of sin and cos doesn't change the value.

Answer 11

thank you so much for your help :)

Answer 12

Erin, it's not that I found the first point and then the second, but rather that I found both coordinates of the terminal point. Just as you need both a radius and an angle in a polar coordinate system, you need both x and y here. If you only have one, you're describing a line; with both, the point is the intersection of the two lines (one is y = the y value, the other is x = the x value).

Answer 13

yes, i understand how you found it now. i just didn't do a great job of explaining it. thank you so much once again :)