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Physgeek64
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Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx??
much appreciated :) :)
much appreciated :) :)
Well no. Your first hint as to why it isn't a GP is that if it were, we would most definitely be applying the formula for the GP of an infinite sum. That would then mean that sin(x) could be easily represented as a simple fraction in terms of x and that would change everything in maths.Physgeek64 said:ahh okay! we're getting round to this in maths after had term. does it set up a GP??
x-x3/3 :)Physgeek64 said:so would it end up as x+(x^3/3) as an approximation?? xx
okay. Thank you so much! I'm doing these physics papers and they're non-calculator and a lot of the involve using sin and cos for non-standard angles. Is there one for tan as well?? xxMentallic said:Well no. Your first hint as to why it isn't a GP is that if it were, we would most definitely be applying the formula for the GP of an infinite sum. That would then mean that sin(x) could be easily represented as a simple fraction in terms of x and that would change everything in maths.
Your second hint is that if you divide the first by the second term, the second by the third, etc. you won't get the same result each time, so it can't be a GP.x-x3/3 :)
I'll take that smiley as an exclamation point!Mentallic said:x-x3/3 :)
Aside from using sin/cos, there is this:Physgeek64 said:Is there one for tan as well??
Yes that's exactly what I was aiming for haha.Scott said:I'll take that smiley as an exclamation point!
[itex]x-{x^3 \over 6}[/itex]
The equivalent of cosx=1-(x^2/2) for the sin function is sinx=x-(x^3/6).
The equivalent of cosx=1-(x^2/2) for the sin function can be derived using the Taylor series expansion for both cosine and sine functions.
Yes, the equivalent of cosx=1-(x^2/2) for the sin function can be used to approximate sine values for small values of x.
Yes, there are other equivalent formulas for the sine and cosine functions, such as the Maclaurin series expansion, which includes higher order terms and provides a more accurate approximation.
An equivalent formula for the sine function allows for easier calculation and approximation of sine values, which is useful in various mathematical and scientific applications.