Thread: Quite an easy trig identity question - need pointers

Hello,

I am trying to do the following question. I've just done a chapter which involved trig identities but apparently this one involves coordinate geometry though I'm not sure.

Using the identities in your notes, express the following in terms of the sines and cosines of x, y, 3x and 3y.
i) sin(3x - y)
ii) cos (x + 3y)

I realise this is probably a silly question but I just don't know how to go about it.
for the first one, I know that sin(theta) = -sin(-theta), but i'm not sure that is releavant. I also know that sin squared theta + cos squared theta = 1, but I don't know how to manipulate the equations I've been given or what they mean.

Any help at all is appreciated, many thanks in advance.

There are formulas for the sine and cosine of sums and differences: see Wikipedia and MathWorld. I would expect that these formulas should be derived or given in class. You can also Google, for example, for "sine sum" to find the derivations.

Have you learnt about the addition formulae in your math class?
sin(A-B) = sinAcosB - cosAsinB
cos(A+B) = cosAcosB - sinAsinB.

I am not sure what the question wants but it may be useful to you.

Originally Posted by arccos

Have you learnt about the addition formulae in your math class?
sin(A-B) = sinAcosB - cosAsinB
cos(A+B) = cosAcosB - sinAsinB.

I am not sure what the question wants but it may be useful to you.

thank you, I'd forgotten about that. so, I can write:
sin (3x - y) = sin3xcosy - cos3xsiny ?

can I do anything else to it?

Using the identities in your notes, express the following in terms of the sines and cosines of x, y, 3x and 3y.
i) sin(3x - y)
ii) cos (x + 3y)

I think that's the simplest you can simplify it down to, and it has satisfied your question.
Remember to use brackets to make it easier to interperet.

sin(3x - y) = sin(3x) cos(y) - cos(3x) sin(y)

You could use the triple angle formulas but that just makes it more complicated.

Originally Posted by Educated

[snip]

You could use the triple angle formulas but that just makes it more complicated.

...and unnecessary, as the problem makes it clear having the angles 3x and 3y is fine.

Originally Posted by foggynotion

thank you, I'd forgotten about that. so, I can write:
sin (3x - y) = sin3xcosy - cos3xsiny ?

can I do anything else to it?

That would be sufficient to fit within the parameters of the question.