The Student Room Group

C3 - Further Trigonemetric Identities Help needed

Alrite guys,

I've been trying to get these questions done for a while now and still no luck. Hopefully someone can help.. :smile:

20a) express 1.5 sin 2x + 2 cos 2x in the form R sin(2x+a), where R>0 and 0<a<90. a=alpha

b) express 3 sinx cosx + 4 cos^2x in the form a sin2x + b cos2x + c, where a,b and c are constants to be found.



And finally,

18c) Find all solutions in the range 0<x<180 of the equation cos2x-cos4x=sinx
As a starter i worked out in the previous part b of the question that
cos2x- cos4x=2sin3xsinx .

Thanks for any help at all.

Chris
Reply 1
Right i think i've done most of question 20a but the books giving me a slightly different answer to what i've got which i'm sure is right.

20a) 1.5 sin2x + 2cos2x

R sin(2x+a) = R sin2x cosa + R sina cos2x
R cos a =1.5
R sin a =2

Rsina/Rcosa=2/1.5
tan a=2/1.5
a=53.13
R=1.5/cosa=2.5

Answer= 2.5sin(2x + 53.13)

however the book seems to think its 2.5sin(2x+0.927)

Anyone got any suggestions?
Reply 2
Whats 53.13 in radians :p:. You gotta look at the question usually specifies what the angle will be in.
Reply 3
Yeh good point, forgot that they could still be in radians.

Could anyone have a go at 20b)?
Reply 5
Thanks a lot steve, makes a lot of sense now.

Now to finish off, would anyone be kind enough to finish off 18c)? :smile:

Cheers
Reply 6
c013310
Thanks a lot steve, makes a lot of sense now.

Now to finish off, would anyone be kind enough to finish off 18c)? :smile:

Cheers


Here...
Reply 7
Thanks again
Reply 8
where did the cos2x+1 come from?