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Knowledge of C3 Proofs (Edexcel)?

Does anybody know what formulas could potentially be asked to be proved in edexcel c3?

I am pretty sure you need to know the pythagorean ones (the ones with inverse trig ratios squared), but I am wondering about any others. Mainly the R formula, with Asinx + Bcosx = Rsin(x+alpha). Thank you :smile:
Reply 1
Avatar for Zacken
Zacken
22
Original post by jamb97
Does anybody know what formulas could potentially be asked to be proved in edexcel c3?

I am pretty sure you need to know the pythagorean ones (the ones with inverse trig ratios squared), but I am wondering about any others. Mainly the R formula, with Asinx + Bcosx = Rsin(x+alpha). Thank you :smile:


Do you know how the R formula is derived? Just expand the sin(x +alpha), that gets you R(sin x cos alpha + sin alpha cos x)

Then expand again: A sin x + B cos x = Rsin x cos alpha + R cos x sin alpha. Compare coefficients:

A = R cos alpha

B = R sin alpha

So to find R, A^2 + B^2 = R^2(sin^2 alpha + cos^2 alpha) = R^2. Hence A^2 + B^2 = R^2.

B/A = (Rsin alpha)/(R cos alpha) = tan alpha. So alpha = tan^(-1) (B/A).

Same thing for Rcos(x + alpha).
Reply 2
Avatar for jamb97
jamb97
OP
2
Original post by Zacken
Do you know how the R formula is derived? Just expand the sin(x +alpha), that gets you R(sin x cos alpha + sin alpha cos x)

Then expand again: A sin x + B cos x = Rsin x cos alpha + R cos x sin alpha. Compare coefficients:

A = R cos alpha

B = R sin alpha

So to find R, A^2 + B^2 = R^2(sin^2 alpha + cos^2 alpha) = R^2. Hence A^2 + B^2 = R^2.

B/A = (Rsin alpha)/(R cos alpha) = tan alpha. So alpha = tan^(-1) (B/A).

Same thing for Rcos(x + alpha).
Yes I am aware of how they are derived, I am wondering if that could be asked in the exam though
Reply 3
Avatar for Zacken
Zacken
22
Original post by jamb97
Yes I am aware of how they are derived, I am wondering if that could be asked in the exam though


*shrugs* probably not. Just know your stuff and you'll be fine, honestly.

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