Q. Trig (1 Viewer)

[ezzy85]

Find k in terms of n if sin n@ + sin(n-2)@ = 2sin k@ cos@

This q has 3 parts to it, thats part 1. I was hoping to work this out before attempting the rest.
Thanks

 

[ND]

Hint: Use the trig identity sinU+sinV = 2sin((U+V)/2)cos((U-V)/2).

 

[ezzy85]

thanks.
i thought if you use that, theyd tell you since that its not in the course apparently.

 

[turtle_2468]

I think sums to products is actually in the course, check to see if I'm mistaken...

 

[Newbie]

my teacher told me it wasnt in the course

 

[ND]

I don't think it's actually in the syllabus, but you do need it for some 4u (and harder 3u) questions (like those polynomial/complex roots of unity q's).

 

[Affinity]

it's in the course.. think it's in the 3U course..
Anyway, Just because it's not in the course doesn't mean it's not mathematics.

 

[Richard Lee]

Originally posted by ezzy85
Find k in terms of n if sin n@ + sin(n-2)@ = 2sin k@ cos@

This q has 3 parts to it, thats part 1. I was hoping to work this out before attempting the rest.
Thanks

Answer:
If @=(m+1/2)*pie, m is natural, then k can be any natural number
If @=/=(m+1/2)*pie, k*@=m*pie+(-1)^m*(n-1)*@
when m=0, k=n-1

 

[Xayma]

Originally posted by Affinity
Anyway, Just because it's not in the course doesn't mean it's not mathematics.

As my maths teacher has said anyway, it all carries on, you learnt how to add in kindergarten and you are still using that (unless you are totally dependent on your calculator).