Small angle approximation help

nootnoot12001

I've got no idea how to do this - how do you find the small angle approximation of cos^2 x?
I know the small angle approximation of cos x is 1 - (x^2)/2 , but don't know how to get from that to this.

Reply 1

Tgm11801

Cos^2x is the same as (cosx)^2, does this help?

Reply 2

nootnoot12001

Original post by Tgm11801

Cos^2x is the same as (cosx)^2, does this help?

I know that - I just don't know how to square 1 - (x^2)/2 properly.

Reply 3

Tgm11801

Just use the FOIL method or whatever method you would usually use to expand 2 brackets

Reply 4

RDKGames

Study Forum Helper

Original post by nootnoot12001

I know that - I just don't know how to square 1 - (x^2)/2 properly.

As above, you can just use FOIL to square it... or even use the grid method, whatever works for you.

Though note that since

\theta

is small and you ignore powers of it greater than 2, it means you can ignore the

\theta^4

term.

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