Degrees or Radians modelling?

I was doing question 9 from the 2022 Edexcel A-Level paper 2 (https://www.mathsgenie.co.uk/alevel/a-level-pure2-2022.pdf) and I was wondering why you would use degrees instead of radians I thought you always use radians in calculus? (I used differentiation to get one of my values)

Reply 1

george flowberry

Original post by glitzz1

the model's in degrees so you use degrees: H = Asin(bt + α)°

Reply 2

DFranklin

Original post by glitzz1

You don't need to use calculus. Maximum value of R sin(kx + a) is R (because the maximum value of sin is 1). Similarly for cos.

If you differentiated without converting to radians, you probably got a derivative 180/pi bigger than it should be. But if you were just looking for where the derivative is zero this wouldn't actually matter in terms of getting the right answer. I'd expect it to lose you method marks though.

Reply 3

glitzz1

Omg i didnt realise thank you

Reply 4

glitzz1

Original post by DFranklin

You don't need to use calculus. Maximum value of R sin(kx + a) is R (because the maximum value of sin is 1). Similarly for cos.
If you differentiated without converting to radians, you probably got a derivative 180/pi bigger than it should be. But if you were just looking for where the derivative is zero this wouldn't actually matter in terms of getting the right answer. I'd expect it to lose you method marks though.

I understand how to do it that way - but in the mark scheme it says

why is it 'in fact okay'??

Reply 5

glitzz1

Original post by DFranklin

You don't need to use calculus. Maximum value of R sin(kx + a) is R (because the maximum value of sin is 1). Similarly for cos.
If you differentiated without converting to radians, you probably got a derivative 180/pi bigger than it should be. But if you were just looking for where the derivative is zero this wouldn't actually matter in terms of getting the right answer. I'd expect it to lose you method marks though.

also this was my working

is it wrong because once you use radians to find the value of A and you plug it back into the original equation in degrees you would change the calculator to degrees?

Reply 6

davros

Original post by glitzz1

also this was my working

is it wrong because once you use radians to find the value of A and you plug it back into the original equation in degrees you would change the calculator to degrees?

Your expression for dH/dt is only valid if t (and therefore bt + a) is measured in radians. Since the question specifically tells you that bt+a is an expression in degrees, your dH/dt is wrong! But as pointed out, you really shouldn't be using calculus for this question :smile: