Question

Solve trig equation by squaring each side of the equation...can you check if im doing it right so far? http://bamboodock.wacom.com/doodler/7360631c-e5b2-46b0-8a3d-ab4f5986eb8f

Answer 1

yeah, you are doing right:)

Answer 2

okay!

Answer 3

have you solved it further?

Answer 4

almost !!

Answer 5

great:D

Answer 6

is this right>

Answer 7

is the steps correct?

Answer 8

@lsugano what's cos 90 or cos \(\pi/2\)?

Answer 9

0

Answer 10

cos(x)=0 or 1-cos(x)=0
x= , ,.. or cos(x)=1
x=...,...,.. or x= ..,..,,,
can you find thoses angles ?

Answer 11

so the equation
\[\cos x=0\]
the solution is
\(x=\pi/2\)
but there is one more equation
\[1-\cos x=0\]
what;s the solution of this one?

Answer 12

what...why is there 1-cosx = 0? where did that come from

Answer 13

(a)(b)=0 is equivalent to a =0 or b=0

Answer 14

if you have an equation
\[(x+1)(x+2)=0\]
so we have either
\[x+1=0\] or
\[x+2=0\]
so both x=-1 and x=-2 are the solutions
the same technique is applied here
\[2 \cos x(\cos x-1)=0\]
either \(\cos x=0 \) or \(\cos x-1=0\)

Answer 15

do you get this?

Answer 16

YES wait i will draw it out so you can check it !

Answer 17

cool:)

Answer 18

yeah, it's correct. Now solve it further

Answer 19

so i got here

Answer 20

go on ! You're "looking for" x

Answer 21

like this!???

Answer 22

yeah correct, what's the solution for
\[\cos x=1\]

Answer 23

i looked at the unit circle (1,0) cosx=1 so x=0 ?

Answer 24

yeah, you're correct:)

Answer 25

and 2 pi

Answer 26

yes 2\(\pi\) as well

Answer 27

oh but its o≤x<2pi we stilll include 2pi?

Answer 28

sorry ! I didn't see that !

Answer 29

you haven't finished yet !

Answer 30

you need to check if those values are really solutions !
plug them in the original equation !

Answer 31

like this...?

Answer 32

yes ! for all those values !(0,pi/2,3pi/2)
and you didn't ask me why you should check !

Answer 33

we check because not all are solutions of the equation and 3pi/2 is -1 so its not a solution!!!

Answer 34

But ! We don't do that,always !
this equation ! you could do it differently ! remember that questions about
cos(x)+sin(x)=ksin(x+alpha)
it can be useful !

Answer 35

okay!!

Answer 36

if you solved it that way ! You don't have to check !

Answer 37

thank you!! saved me!