Question

Need help understanding solving trig equations pls

Answer 1

\[-2\cos(3x)=-1\]

Answer 2

@AloneS

Answer 3

dicide everythg by -2..

Answer 4

\[\cos(3x)=1/2\]

Answer 5

now cos of what angle is 1/2?

Answer 6

pi/3 right

Answer 7

oh and the interval is [0,2pi)

Answer 8

yes, then 3x=pi/3

Answer 9

so x=pi/9?

Answer 10

is x in [0 2pi]?

Answer 11

yes

Answer 12

so you would have one more solution because
cos(300)=cos(60)=1/2

Answer 13

cos(300)?

Answer 14

oh cuz 360-60 right

Answer 15

yes

Answer 16

cos(300)=cos(60)?

Answer 17

i dont understand that

Answer 18

use this trig relation:
cos(2pi-a)=cos(a)
now let a be 60 ..

Answer 19

2pi-60

Answer 20

2*180-60=300

Answer 21

oh ok

Answer 22

so whats the next step?

Answer 23

or in radians, 5pi/3

Answer 24

there is no more step as you have solved for x.

Answer 25

is there no other solution?

Answer 26

in [0 2pi]? no

Answer 27

ok so do we not do anything with 5pi/3?

Answer 28

you have found two solutions, pi/3 and 5pi/3. period

Answer 29

ok thanks so much :D

Answer 30

never mind. good luck with your studies!

Answer 31

hey, i'm sorry we did somehing wrong

Answer 32

:o

Answer 33

I don't use any pen right now so you should have told me we were doing somethig wrong.

cos(3x)=1/2
3x=pi/3 --< x=pi/9
3x=5pi/3--> x=5pi/9

Answer 34

ok but i dont th ink you can use 5pi/9 cuz its in the quad where cos is negative

Answer 35

im so sorry i have to go im at school rn thx for helping tho

Answer 36

cos(5pi/9) is negative but cos(3x) where x=5pi/9 NOT!

Answer 37

see you