Question

Find all values of x between 0 and 4pi

Cos(x)= -0.6591

Answer 1

Could someone please explain it to me. Thank you

Answer 2

use ur calculator and find Cos^-1 -0.6591
cause cos <0 so im sure that X will be at Quadrant II or III

Answer 3

I did that but there are 3 other values I need to find within the 0 and 4 pi restriction

Answer 4

How can I find the other three?

Answer 5

What is the rule I need to follow? Cheers

Answer 6

\(\large \mathbb{\cos (x) = \cos(x + 2\pi ) }\)

Answer 7

that gives u 2nd solution

Answer 8

I don't get it

Answer 9

wat did u get for first value ?

Answer 10

Where did you come up with cosx = cos(x+2pi)

Answer 11

from many places.
for now u can think of it like this :
period of cosx = 2pi, so it repeats every 2pi.

Answer 12

I got 2.290

Answer 13

yes,

use the given property now.

second solution = \(2.29 + 2\pi\)

Answer 14

if x is a solution, then x+2pi is also a solution.
cuz cos(x) repeats every 2pi.

Answer 15

if that makes any sense..

Answer 16

I see what about the other two values?

Answer 17

It does

Answer 18

good :)
for other two values, use another property :

\(\large \cos(x) = \cos(-x)\)

Answer 19

let me show it in a picture, so it makes sense why this is true.

Answer 20

u familiar wid 'unit circle' definition of trig functions ?

Answer 21

Yep

Answer 22

then its easy for u,