Question

Find all theta in the interval [0, 2pi) that satisfy the equation.

2costheta*tantheta + tantheta = 0

I know you can simplify that to
tantheta(2costheta +1) = 0
but I don't really understand what to do next...

Answer 1

now solve for tan =0 and 2cos+1=0

Answer 2

tan takes on values of 0 at (0, pi, and 2pi) to solve for cos=-1/2

Answer 3

think in what quadrant is cos = to a negative answer

Answer 4

do you want to try or would you just like the answer?

Answer 5

well, see i know what the answers are, i just don't understand how to get to them. they're 0, 2pi/3, pi, and 4pi/3

Answer 6

i'll draw a picture

Answer 7

haha thanks

Answer 8

120 degrees =2pi/3 and 240 degrees is 4pi/3

Answer 9

cos = -0.5 only for 60 degrees but in quadrants 2 and 3 therefore you have to +- 180 because we always start at the far right in quadrant 1 at 0

Answer 10

ohhh okay i get it now, thank you!