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# sin theta ~ tan theta ~ theta. HELP watch

1. at the back of my (edexcel) physics paper

it says

sin theta ~(roughly equal to) tan theta ~ theta
cos theta ~ 1

i dont understand.
can anyone explain it?

thanx
2. If you use the series expansions you get
sinx = x - (x^3)/3! + (x^5)/5! - ....
cosx = 1 - (x^2)/2! + (x^4)/4! - ....
For small x, x^3 terms and above can be neglected so sinx ~ x, cosx ~ 1 - (x^2)/2! More roughly if you neglect x^2 terms, cosx ~ 1. tanx = sinx/cosx ~ x
3. (Original post by scarlet ibis)
at the back of my (edexcel) physics paper

it says

sin theta ~(roughly equal to) tan theta ~ theta
cos theta ~ 1

i dont understand.
can anyone explain it?

thanx
These are the assumptions to make if theta is very small.
4. look at their graphs and draw the graph y = x

or alternatively use the mclaurin expansions

sinx = x - x^3/3! + x^5/5! .. etc

you can see that when x is small, the terms after x will become negligible, and sin x = x

same argument can be used to show that cos x = 1 for small x

and tan x = sin x/cos x ... for small x, numerator = x for small x, denominator = 1 for small x, so tan x = x/1 = x for small x.
5. (Original post by Bezza)
If you use the series expansions you get
sinx = x - (x^3)/3! + (x^5)/5! - ....
cosx = 1 - (x^2)/2! + (x^4)/4! - ....
For small x, x^3 terms and above can be neglected so sinx ~ x, cosx ~ 1 - (x^2)/2! More roughly if you neglect x^2 terms, cosx ~ 1. Can't remember how you do tanx though

Bloody hell yer quick
6. (Original post by fishpaste)
Bloody hell yer quick
Wasn't much quicker than you! And I forgot how to do tanx to start with
7. thanks. i think i understand, but i don't do maths, so its still be bit hard to grasp
8. (Original post by scarlet ibis)
thanks. i think i understand, but i don't do maths, so its still be bit hard to grasp
Indeed. In fact you don't learn where those expansions/approximations come from unless you do further maths! Never really used in the alevel. But they're useful in physics for things like SHM I guess.
9. Also remember that that's for theta in radians and not degrees.

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