Trigonometry Help

Problem posted in a picture.

Question

Trigonometry Help

Problem posted in a picture.

anonymous · Answer

attachment

anonymous · Answer

I can get as far as (2sinx cosx)cosx + sinx =0
                             2sinx cos^2 x + sinx = 0

anonymous · Answer

After that, im not too sure what to do

ikram002p · Answer

2sinx cos^2 x + sinx = 0 
=sin x (2 cos^2 x +1 ) =0
sin x =0
or 
2cos^2 x +1 =0

anonymous · Answer

alright so i did that part right then.
can you help me work out the 2cos^2 x + 1 = 0?

ikram002p · Answer

2 cos^2(x) - 1 = cos 2 x 
add +1 to both sides

cos 2x+1 = 2 cos^2 x

@ganeshie8  there is something wrong  ,right ?

ikram002p · Answer

@nsellers23  complex numbers allowed ?

anonymous · Answer

no i dont think so

anonymous · Answer

sorry, not really understanding how you got 2cos^2(x) = cos2x
where did the cos2x on the right come from?

ikram002p · Answer

then the only solution when 
sin x =0 :)

ganeshie8 · Answer

2cos^2 x +1 =0

cos^2x = -1/2

No solutions.

ganeshie8 · Answer

sinx = 0 is the only equation u need to solve

anonymous · Answer

yeah so my answers would be 0,2pi?

ikram002p · Answer

ur interval is [0,2pi)
check ) means 2pi is not in ur interval

anonymous · Answer

ooooh thats true cause the ) means up to but not including
forgot about that

ikram002p · Answer

:)

anonymous · Answer

hm it tells me there is one more solution other than 0

ganeshie8 · Answer

sinx = 0 should give you two solutions

ganeshie8 · Answer

sin 0 = 0
sin pi = ?

anonymous · Answer

yeah it would be 0 and 2pi

ganeshie8 · Answer

nope, 2pi is not in the given interval... so 2pi is not a solution

ganeshie8 · Answer

0 and pi are the solutions.

anonymous · Answer

do you mind explianing why pi is the solution? i come out with 2pi so how do you decide it to be just pi?

ganeshie8 · Answer

short answer :

pi is a solution because
sin(pi) = 0

anonymous · Answer

lol alright, that makes sense actually.

ganeshie8 · Answer

this is one of those values which we're expected to memorize when doing trig course...  :)

anonymous · Answer

yeah theres not very many of those :\ ....not, lol theres so much memorizing in trig

anonymous · Answer

well thanks guys/girls, both of you. moving on to the next problem, ill come back if i need anymore help. you were both huge help :D

ganeshie8 · Answer

good luck !

ikram002p · Answer

np :)
ur wlc @nsellers23  
and good luck ^

anonymous · Answer

@ikram002p how can i simplify sinx+2cosx+1?

anonymous · Answer

|dw:1404777438187:dw|

anonymous · Answer

ill open a new problem, no worries.