Question

Why is the cosine and sine of -5pi/3 (1/2, sqrt(3)/2 respectively?

Answer 1

I thought it'd be: \[-\frac{ 1 }{ 2 }, \frac{ -\sqrt{3} }{ 2 }\]

since 5pi/3 is in the 3rd quadrant and both cosine and sine are negative.

Answer 2

@SolomonZelman

Answer 3

no look at the unit circle again

Answer 4

Oh yeah I mean 1/2, -sqrt(3)/2

Answer 5

it's negative 5pi/3
but you're thinking about positive 5pi/3

Answer 6

the easy way is add 2pi to make it positive
-5pi/3+2pi = pi/3 which is in first quadrant so that's why

Answer 7

how does the negative sign affect it?

Answer 8

to*

Answer 9

ohh like coterminal?

Answer 10

yeaho

Answer 11

ohh ok thank you!

Answer 12

what about sin t= 4/5
sin(pi - t) and sin(t + pi)

Answer 13

The negative angle tells you to go in a clockwise direction instead of counter-clockwise like normal

Answer 14

np :) good work!
for me its easy to add 2pi or 360
but some people like to keep going around the circle

Answer 15

yea that ^^

Answer 16

`what about sin t= 4/5`
`sin(pi - t) and sin(t + pi)`

use these identities

sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)
sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B)
sin(pi) = 0
cos(pi) = -1

You'll need to figure out what cos(t) is equal to. Hopefully it tells you which quadrant angle t is in?