Fp2 integration

Sketch the graph and the cord, sketch the line 1-x then find and sketch the tangent. What do you observe?

the graph cos(x)-sin(x) is 'sandwiched' between the the chord and the line 1-x, tangent of what?

The chord is 1-x, isn't it? I'm in bed and don't have my glasses on but that's what it seems like to me. Tangent at p, what's the equation of the tangent at P?

y=-1(x-pi/4) rearranged to give me y=pi/4(1-4x/pi), not seeing how the cord is y=1-x with the intersection at pi/4, although i could be misreading

The chord is the line connecting P and Q, what's the equation of that?

been looking at not now, but it looks like the line y=1-4x/pi fits the criteria, which means i need to re look at the equation of the tangent EDIT: found the tangent form the wrong point, its y=1-x

LOL. I can't read apparently. I thought the pi was something else

So the curve being sandwiched gives rise to the inequality

Yeah this question is actually pretty neat , although it would be a bit s*** to get this in under exam conditions

Sounds very part (i) of a STEP question-esque. I know of one that uses the same concept as this in a very different context, you'd enjoy it. Remins me tomorrow, I'm in bed now.

Edit: don't think you'd get something like thisnis an exam.

will do, PRSOM it has ocr at the bottom, which means they put it in an exam although it has an asterix so they must have felt it was too hard when everyone's scores plummeted

Possibly it was in an exam a few years ago when standards were higher or such. The edexcel textbook is the same! They have "examination question" that make recent papers look a doddle.

Wouldnt mind a return to those standards, A's for FP2/3 are already ~55/72 going even further down gives me more room for silly errors

A year or two ago, it was 71/75 for an A* in FP2... wtf.
Even this Jan, the S2 exam that I sat, it was 70/75 for an A*...

A year or two ago, it was 71/75 for an A* in FP2... wtf.
Even this Jan, the S2 exam that I sat, it was 70/75 for an A*...

Those UMS jumps are horrendous, congrats on your results btw, as for M3.... luckily you took s3 as an insurance

http://filestore.aqa.org.uk/over/stat_pdf/AQA-A-LEVEL-GDE-BDY-JUNE-2015.PDF

Greatest exam board ever

Sketch the graph and the cord, sketch the line 1-x then find and sketch the tangent. What do you observe?

I guess that they're looking for a graphical approach, given that this is an A level question, though the question doesn't make it clear. I think that you can also show that the inequality holds by considering the gradient of $\cos x-\sin x=\sqrt{2}\cos(x+\frac{\pi}{4})$ over the interval, though I found the argument for the lower inequality tricky to get right (late last night, at least).