A Level Trig Help

"Given that theta is small, show that
Cos(4theta) - Sin(2theta) ~= 1 - 2theta - k(theta²)"

Does anyone know how to do this? I'm pretty sure it's the double angle formula but I'm unsure how to like use it. Any help would be appreciated

Reply 1

DFranklin

You don't need double angle formulae. Just use the standard small angle approximations.

Reply 2

MWorldwide19

Original post by DFranklin

You don't need double angle formulae. Just use the standard small angle approximations.

I don't think I've learnt that, what is it

Reply 3

DFranklin

Original post by MWorldwide19

I don't think I've learnt that, what is it

https://en.wikipedia.org/wiki/Small-angle_approximation

You should have learnt it - the question is basically impossible without it.

Reply 4

Jam.123

Use these for questions like this (

\theta

must be in radians):

\sin\theta \approx \theta

\cos\theta \approx 1 - \frac{\theta^2}{2}

\tan\theta \approx \theta

Read this for the derivations (which should be known so don't skip!):
https://brilliant.org/wiki/small-angle-approximation/

You should be able to figure out your question from there.

Reply 5

MWorldwide19

Original post by DFranklin

https://en.wikipedia.org/wiki/Small-angle_approximation

You should have learnt it - the question is basically impossible without it.

Thanks, that really helps. Don't know why I never learnt it

Reply 6

MWorldwide19

Original post by Jam.123

Use these for questions like this (

\theta

must be in radians):

\sin\theta \approx \theta

\cos\theta \approx 1 - \frac{\theta^2}{2}

\tan\theta \approx \theta

Read this for the derivations (which should be known so don't skip!):
https://brilliant.org/wiki/small-angle-approximation/

You should be able to figure out your question from there.