Question

Find the terminal point determined by t= 10pi/3.

I somewhat understand how to get the answer, but any extra help would be greatly appreciated.

Answer 1

since this is on the unit circle, this means we can find any point of the form (x,y) where

x = cos(t)
y = sin(t)

where t is the angle

Answer 2

for example, if the angle was pi/3, then

x = cos(t)
x = cos(pi/3)
x = 1/2

y = sin(t)
y = sin(pi/3)
y = sqrt(3)/2


This means that the terminal point for t = pi/3 is (1/2, sqrt(3)/2)

Answer 3

Alright, so because I have 10pi/3, I would us pi/3 for the points?

Answer 4

no pi/3 was just a similar example

Answer 5

you would need to evaluate the cosine of 10pi/3 to get the x coordinate of the terminal point

Answer 6

and you would need to evaluate the sine of 10pi/3 to get the y coordinate of the terminal point

Answer 7

make sense?

Answer 8

btw

10pi/3 is over 2pi, so you can subtract 2pi from it to get


10pi/3 - 2pi

10pi/3 - 6pi/3

(10pi - 6pi)/3

4pi/3

Answer 9

this means that the angles 10pi/3 and 4pi/3 are coterminal angles

Answer 10

I'm still pretty confused about it.
Why is 10pi/3 over 2 pi?

Answer 11

well I used a calculator to get 10pi/3 = 10.471975511966 and noticed it's larger than 6.28 (which is what 2pi is roughly equal to)

Answer 12

Okay then why would I subract 2pi?

Answer 13

2pi radians is the same as 360 degrees

Answer 14

so if you add or subtract 2pi radians, you'll do a full 360 degree revolution and go from one angle and land on itself more or less

Answer 15

ex: start at 0 degrees...add on 360 to get 0+360 = 360 degrees and you'll end up at the same spot

Answer 16

so that's is why we can say that 10pi/3 and 4pi/3 are effectively the same angle

Answer 17

Oh! So if instead of 10pi/3, I had something like 14pi/7, I would be able to subtract 2pi toget the terminal points?

Answer 18

14pi/7 reduces to 2pi

Answer 19

and you could leave it as 2pi or you can subtract 2pi from it to get 2pi - 2pi = 0pi = 0

this shows us that 0 and 2pi are coterminal points (ie effectively they are the same angle)

Answer 20

@jim_thompson5910 , you are an absolute angel. Thank you so much!

Answer 21

sure that's not "angle" lol jk

glad I was of help though

Answer 22

anyways, though, this may be very helpful

http://www.regentsprep.org/Regents/math/algtrig/ATT5/600px-Unit_circle_angles_svg.jpg

Answer 23

that's the unit circle and you'll see at 4pi/3 the point ( -1/2, -sqrt(3)/2) ), which is the terminal point for 10pi/3 (and 4pi/3)

Answer 24

Thank you again :)

Answer 25

sure thing