Thread: Help

There's a task in my math book that says:
Write the expression

\/2*(cos(3x+ π/4))

using cos3x and sin3x. (\/2 means the square root of 2, I couldn't locate the square root sign on my keyboard).

I ended up with \/2*(cos3x-sin3x), but the answer is supposed to be cos3x-sin3x. What did I do wrong?

Oh, and, sorry if my translation makes no sense. I'm Norwegian and not very used to talk about mathematics in any other language than Norwegian

Originally Posted by daniel

There's a task in my math book that says:
Write the expression

\/2*(cos(3x+ ?/4))

using cos3x and sin3x. (\/2 means the square root of 2, I couldn't locate the suare root sign on my keyboard).

I ended up with \/2*(cos3x-sin3x), but the answer is supposed to be cos3x-sin3x. What did I do wrong?

Oh, and, sorry if my translation makes no sense. I'm Norwegian and not very used to talk about mathematics in any other language than Norwegian

Am I to assume your "n" is supposed to be pi?

If so, then that's the problem.

cheers
william

Yeah, I just copied the pi sign from a website and it showed up mysteriously similar to an "n" here. How is that the problem?

Okay, not really the problem so much as the "solution".

cos(pi/4) = sqrt(2)/2 = sin(pi/4)

sqrt(2)*sqrt(2)/2 = 1

and your troublesome coefficient disappears.

Hope that helps,
william

I assume you're using
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
by the way....

cheers

Well, it says cos(3x+pi/4), not cos(pi/4)
Here's what I did to reach the answer I got:
sqrt2*(cos(3x+ pi/4))
=
sqrt2*(cos3x*sin(pi/4) - cos(pi/4)*sin3x)
=
sqrt2*(cos3x - sin3x)

Oh, snap, I just got understood why the sqrt2 goes away. Thanks for your excellent assistance to my enlightenment, dear William.

Originally Posted by daniel

Well, it says cos(3x+pi/4), not cos(pi/4)
Here's what I did to reach the answer I got:
sqrt2*(cos(3x+ pi/4))
=
sqrt2*(cos3x*sin(pi/4) - cos(pi/4)*sin3x)
=
sqrt2*(cos3x - sin3x)

You're confusing cos(a+b) with sin(a+b)...
and what you wrote indeed says "cos(pi/4)" (and sin(pi/4)) no?
(But you still need to use the correct trig identity....)

cheers

Originally Posted by daniel

Oh, snap, I just got understood why the sqrt2 goes away. Thanks for your excellent assistance to my enlightenment, dear William.

No problem.
But make sure you use the correct trig identity. It looks like you are using the one for sin(a-b)....

cheers

Originally Posted by william

You're confusing cos(a+b) with sin(a+b)...

Ah, yes, I didn't see that until now ^_^