Question

HELP PLEASE!!!
What is the solution set of the equation 2 cos^2 data- cos data =0 over the interval 0 degrees < or equal to data < 360 degrees?

Answer 1

Not sure why the variable is called "data" but its the same as:
\[2\cos^2x \space - cosx = 0 \space \space , 0 \le x <360\]

Answer 2

right? This is the same equation?
So we could solve this with factoring, do you see how to proceed in that direction?

Answer 3

nope, not at all

Answer 4

btw the answer is
{60, 90, 270, 300} degrees

Answer 5

and again, please help me still, cause i don't don't know how the heck to do, please

Answer 6

Is there a GCF?

Answer 7

cosx is common right?

Answer 8

uh cosx?

Answer 9

oh well I guess we both answered it then lol

Answer 10

ok so please continue....

Answer 11

\[cosx(2cosx-1)=0\]

Answer 12

then just set each factor equal to 0 and see what solutions result

Answer 13

I still don't get how the answer is 60, 90, 270, and 300

Answer 14

\[cosx = 0\]
\[2cosx-1=0\]

Answer 15

I don't know what to do from there

Answer 16

Well, are you familiar with the Unit Circle?

Answer 17

yes

Answer 18

so we solve those 2 equations for cosx first

Answer 19

we want to find the angles where cosx=0 and cosx= ..?

Answer 20

0?

Answer 21

first is cosx=0 2nd is different
2cosx-1 = 0
2cosx = 1

Answer 22

so its cosx = 1/2 right?

Answer 23

So we want to find on the Unit circle , the angles that have a cosine of 0, or 1/2
On the Unit circle is it the x, or the y, that corresponds to cosine?

Answer 24

yea

Answer 25

wait wait wait wait wait

Answer 26

it's 1/2 if it's pie over 3
if it's pie over 6, sin is 1/2

Answer 27

The terminal point on the Unit Circle is (cos(theta), sin(theta))
So its the x so I want to see what point has an x=1/2 or an x=0
So I can draw 2 vertical lines x=0 and x=1/2
so where they intersect the unit circle will be our solutions.
But we still have to have a good idea what angles we are looking at

Answer 28

yes so that is pi/3 or 60 deg the first one

Answer 29

wait how u know it's 1/2 again, that's the part i don't get?

Answer 30

cause I thought it could either be 1/2
or radical 3/2
right???

Answer 31

because our solution said cosx = 1/2

Answer 32

on the unit circle that means the x-coordinate of the terminal point is 1/2

Answer 33

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
LOL

Answer 34

I'm so dumb I don't know how to add LOL!!!

Answer 35

Haha

Answer 36

http://prntscr.com/6bnn3e

Answer 37

ok please continue

Answer 38

on the unit circle that means the x-coordinate of the terminal point is 1/2
so I drew a vertical line x = 1/2
and looked to see where it intersected the Unit Circle
and of course I know it will be some multiple of 30 deg
I just have to figure out which qudrant and then if in Quad I, is it 30 or 60? and so on

Answer 39

ok so what about 90, 270, and 300???