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| -rw-r--r-- | Fourier Series.page | 15 |
1 files changed, 4 insertions, 11 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index b2a9246..00ad189 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -6,17 +6,10 @@ We first begin with a few basic identities on the size of sets. Show that the se To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: -$\qquad\qquad\sin^2(x) = ?$ -$\sin^2(x) = ?$ - -$$\begin{array}{ccl} - & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ - & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ - & = & \cos y+i\sin y\end{array}$$ - -$\frac{Numerator}{Denominator}$ - -\tt{Hey what's going man? I'm learning Latex} +$\qquad\qquad\sin^2(x) = ? $ +Based on the double angle formula, $\cos(2x) = 1 - 2 \sin^2(x)$ +Rearranging, +$\sin^2(x) = \frac{1-\cos(2x)}{2}$ ##What is the Fourier series actually?</b> |