Question

find all solutions
2cos(theta)+1=0
write in radians in terms of pi

Answer 1

cos(theta) = -1/2

Understood that?

Answer 2

kinda....

Answer 3

cos theta-1= 0 (add 1 to each side)
cos theta = 1
Look at a graph of the cosine function, and you will see
cos theta = 1 at the points X = 0, and X = 2pi

Answer 4

where are the brackets in this?
if it is (cos x) -1 =0
it is find arccos of 1 in radians ( 0, 2Pi etc)

if it is cos(x-1) =0 it is
(arccos 0) -1 which is -Pi/2, pi/2 etc.

(arccos is inverse cos)

Answer 5

costhetat=1

whre does the costheta equal one?

when theta equals 0 and pi. Use a unit circle

Answer 6

x = 0 || x = 2 pi

Answer 7

im so confused...............

Answer 8

Show the quadrants where cos is -ve.

Answer 9

i understood this

cos theta-1= 0 (add 1 to each side) cos theta = 1 Look at a graph of the cosine function, and you will see cos theta = 1 at the points X = 0, and X = 2pi

Answer 10

So, it should be two angles between, pi/2 and 3pi /2

Answer 11

how would i write that though

Answer 12

This is the full solution,

2cos(theta)+1=0
2cos(theta) = -1
cos(theta) = -1/2

cos is negative in two quadrants. So we will find the "alpha" angle.



cos^-1 (0.5) (Ignore -ve sign on 0.5 for now)

alpha = 1/3 pi

Therefore case 1,


pi - 1/3pi = 2/3 pi

Case 2,



pi + 1/3pi = 4/3 pi

Those are your two angles where 2cos(theta) + 1 = 0.