Question

Trig problem.. find all solutions in the interval [0,360°) 10 cos^2x+11cosx+3=0 plz show steps thanx!

Answer 1

can you factor the equation?

Answer 2

umm yes i think so

Answer 3

ok then do it

Answer 4

I think I factored the left side.... is this correct?
5cosx+3=0 5cosx-3=0

Answer 5

no

Answer 6

honestly?? well how else do I factor out 10cos besides using 5? am I labeling wrong or something?

Answer 7

let u = cosx
can you factor 10u^2 + 11u + 3?

Answer 8

use AC method

Answer 9

you're looking for two integers that when multiplied gives 30 and when added gives 11

Answer 10

found those two integers?

Answer 11

No i'm totally lost on this i think i'll just do a similar problem i'm really dumb at math thnx for working w/ me though.

Answer 12

do 5 and 6 work?

Answer 13

Ohhhh no see what you were doing but I'm doing this. I meant to input that x=____

Answer 14

idk why i didn't think to snip it earlier sorry for the confusion

Answer 15

well, you find x by factoring first, which requires you to do the ac method

Answer 16

can you now factor
10u^2 + 5u + 6u + 3?

Answer 17

"u" is theta?

Answer 18

no, u = cosx.
The reason I let u = cosx is because it's easy to work with that way

Answer 19

you could have done 10cos^2(x) + 5cos(x) + 6cos(x) + 3 but it's alittle bit harder to see

Answer 20

so instead, let u = cosx, so you have
10u^2 + 5u + 6u + 3

Answer 21

hmmm?? I never tried it this way before but is it
(5u+3) (2u+1)

Answer 22

yes.

so can you solve (5u+3) (2u+1) = 0

?

Answer 23

ummm -3/5, -1/2 ???

Answer 24

yes,
u = -3/5 or u = -1/2

but u = cos(x), so
cos(x) = -3/5 or cos(x) = -1/2

can you solve for x?

Answer 25

cos(x)=1/2
x=2pi/3=120° & 4pi/3=240°

Answer 26

it's cos(x) = -1/2

Answer 27

I used the neg sign just forgot to type it but... You know? I think I have it now!!!!! thanxx :) for the help!

Answer 28

no prob