Amath - Futher trigo identities - R formulae HELP

Gerald732 SG

Hey all,

I've been trying very hard to figure out this particular question for quite some time now already. Its gotta do with the R-formulae in further trigo.

Hope anyone here can advice me on how to solve it, cause even my math teacher cant

So here it is:

Solve the following equations for 0< x<360

2 sin x (2 sin x - cos x) = 1

Thanks =)

Mikethm SG

2 sin x (2 sinx - cos x) = 1

4 sin^2 x - 2sin x cos x = 1

4[1/2-1/2 cos (2x)] - sin (2x) =1

2- 2cos (2x) - sin (2x) =1

2 cos (2x) + sin (2x) = 1

Let 2 cos (2x) + sin (2x) = R cos (2x-P)

R = sqrt 5 and tan P = 1/2---> P = 26.56 degree

Therefore sqrt (5) cos (2x - 26.56) =1

cos ( 2x - 26.56) = 1/(sqrt 5)

Edited due to carelessness.

I believe u can continue from here.

Feel free to ask all your A Maths questions here. The tutors here enjoy helping people. Personally, for myself, it is because I wish my students will ask me questions... but they seldom do. :(

Gerald732 SG

Hey thanks a lot!

Didn't expect a respond that fast, it really helped very much! =)

Really cool place to clear my doubts.

However, I don't understand from step 1 to step 2.

"2 sin x (2 sinx - cos x) = 1

4 sin^2 x + 2sin x cos x = 1"

Shouldn't it be 4sin^2x - 2sin xcos x = 1 ?

And also from step 2 to 3.

And from

2- 2cos (2x) + sin (2x) =1

2 cos (2x) - sin (2x) = 1 , also don't make sense to me..

Thanks

TenSaru SG

step 1-2 is just multiplying 2sinx to the terms in the bracket...

From 4-5 intermediate steps are

2-2cos 2x + sin 2x =1

-2cos 2x + sin 2x = -1 (-2 on both sides)

2cos 2x - sin 2x = 1 (multiply by -1 on both sides)

I'm not a tutor by the way =)

TenSaru SG

For Step 2-3, it's all double angle formula

4 sin^2 x + 2sin x cos x = 1

separating the 2 terms,

cos 2x = 1 - 2sin^2 x 2sinx cosx = sin 2x

2sin^2 x = 1 - cos 2x

sin^2 x = 1/2 - 1/2cos 2x

So...

4[1/2-1/2 cos (2x)] + sin (2x) =1

Gerald732 SG

Alright thanks lots!

Managed to get the answers right already xD

Mikethm SG

I see the sign wrongly mah. :P

coz I looking on my smaller monitor as I was installing Windows 7 on my main rig. :P

Will edit my post.