1. ## Trig problem

Help I have spent about 3 days on this one, where I get lost is with the final part of the question

Use standard identities to express sin(3theta+(sqrt/4) in terms of sin theta and cos theta.

My tutor has explained it, but in terms of asuming that I know all the steps that he missed (a bit like here is a matrix, here is the determinate and missing the bits between)
Thanks

2. Originally Posted by dazza67
Help I have spent about 3 days on this one, where I get lost is with the final part of the question

Use standard identities to express sin(3theta+(sqrt/4) in terms of sin theta and cos theta.

My tutor has explained it, but in terms of asuming that I know all the steps that he missed (a bit like here is a matrix, here is the determinate and missing the bits between)
Thanks
If you post the solution you have and flag the steps you don't get, someone will fill in the gaps.

3. Thanks Mr. Fantastic. This is about where I got to

[quote] Use standard identities to express sin(3θ+(π/4) in terms of sin θ and cos θ
as best as I get
sin
(3θ+(π/4))
sin(A+B)=sinAcosB+cosAsinB
the answer that I was given by a colleague
Ans = ((2sin θ cos θ)cos θ)+(sin θ(1-2 sin θ)) cos π/4 + sin π/4 ((1-2 sin θ) cos θ) - ((2 sin θ cos θ) sin θ

so here is where my problem is.

I end up with sin(3θ)cos(π/4)+cos(3θ)sin(π/4)
I need to know that if I am wrong, why and if he is right, how did he get there from where I am or am I just completely on the wrong path

4. Hello Dazza. You are not wrong. You just need to expand more:

You got: $sin(3\theta)cos\frac{\pi}{4} + cos(3\theta)sin\frac{\pi}{4}$

Now make it: $sin(2\theta+ \theta)cos\frac{\pi}{4} + cos(2\theta+\theta)sin\frac{\pi}{4}$

Expand that using the sum-difference formulas (i.e. sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB)
Then expand the double angles.

5. Originally Posted by Gusbob
Hello Dazza. You are not wrong. You just need to expand more:

You got: $sin(3\theta)cos\frac{\pi}{4} + cos(3\theta)sin\frac{\pi}{4}$

Now make it: $sin(2\theta+ \theta)cos\frac{\pi}{4} + cos(2\theta+\theta)sin\frac{\pi}{4}$

Expand that using the sum-difference formulas (i.e. sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB)
Then expand the double angles.
Thanks for that, next dumb one,expand the double angles??

6. $sin(2\theta) = 2sin(\theta)cos(\theta)$

$cos(2\theta) =$
$cos^2(\theta) - sin^2(\theta)$
or $2cos^2(\theta)-1$
or $1-2sin^2(\theta)$

7. Thanks for all of your help Gusbob. I will now follow the flow and work thru the rest of the problems, you have very much filled in a couple of missing steps, once again thanks