Question

Solve the following equation:
cos2x-cosx= 0; for 0≤x<2pi
Please help?

Answer 1

first substitute for cos2x;

cos2x = 2cos^2 x - 1

to give

2cos^2 x - cos x - 1 = 0


now you need to solve this quadratic equation for cos x

Answer 2

can you do that?

Answer 3

Yes! I'm doing it rn

Answer 4

-1/2, right?

Answer 5

I mean, there are two answers: -1/2 and 1, which one do you use? Or both?

Answer 6

thats one solution but thers another

Answer 7

both

Answer 8

That's all you have to do?

Answer 9

remember that the cosine is negative in the 2nd and 3rd segments

Answer 10

no you need values of the angles x

Answer 11

eg one angle whose cosine is 1 is 0

Answer 12

so 0º and 120º?

Answer 13

120º for -1/2

Answer 14

thats 2 but there are more

for cos x = -1/2 there also a value of x in the 3rd quadrant

Answer 15

and they want solution in radians

120 degrees = 2pi/3 radians

Answer 16

How will i know which quadrant i should use though?

Answer 17

theres an easy way to remember