Melody

given cos(π/4 + x) = m

what's the value of sin2x, in terms of m?

How about:

\(cos(π/4 + x) = m\\ cos(\pi/4)cosx - sin(\pi/4)sinx=m\\ \frac{cosx}{\sqrt2}-\frac{sinx}{\sqrt2}=m\\ cosx-sinx=\sqrt2\;m\\ \text{square both sides}\\ cos^2x+sin^2x-2cosxsinx=2m^2\\ 1-2cosxsinx=2m^2\\ -2cosxsinx=2m^2-1\\ 2cosxsinx=1-2m^2\\ sin(2x)=1-2m^2 \)

Very impressive!  That looks really hard !

Thanks Tertre   

You got most of it too    

Got it  

The longest peice could be     15.5,  20.5,  17.4,  16.4,   or   21          added together this is exactly  90.8 inches

So there are 5 different possibilies on how the rope is cut.   (only lenghths are important, not the order thay are cut in)

Rather than spoil everyone's fun I will let you individually work out what these 5 double cuts  are.

Hint:   Let one peice be   a   and another   a+5.      You have to work out the other one.   (5 possibilities.)

\(2\sqrt{1.75+\sqrt3}-(1.75+\sqrt3)\\ \)

I'm coming up blank.

but   sqrt root of 3   is irrational so it is not exactly equal to what you said.  

I cannot see any image.  :/

dg, 

I know it is harder but try to teach without giving final answer whenever it is possible.  (most of the time anyway)

Encourage the kids to tell you what they think that the answer is.

If they do not get back to you them maybe they were only ever interested in the answer (which we do not want to encourage).

Or maybe they have been given all that they need.

Hi Rom,

He told me that these are questions from old mathematics competitions and he is using them to 'study' from because he is going to do this type of test himself.

That is excellent. I did not see that one.

It might be nice if you talk about your questions a little when you post them, I mean what you have tried etc

and let us have the same information as what you have.     (I mean the answer)

That would come across a lot better.    :)

You can move it k units to the left (negative direction)  by replacing x with x+k

You can stretch it vertically  by  by multiplying the whole function (LHS) by a constant.

So what do you think the answer might be.

Here is the graph of      f(x) =cos x