
 express \(\sin(3x)\) in term of \(\sin(x)\).
 express \(\cos(4x)\) in terms of \(\cos(x)\).
 simplify
\[
\sum_{k=20}^{k=20} e^{k\phi}.
\]

solve
 \[
y’=\frac{2t}{1+t^2}, y(0)=0;
\]  \[
y’=\frac{2t}{1t^2}, y(0)=0;
\]  \[
y’=\frac{2t}{1t^2}, y(2)=0.
\]
 \[
 solve
 \[
y’=\frac{2x^24x+3}{x1}, y(0)=2;
\]  \[
y’=\frac{x^24x+3}{x2}, y(0)=2;
\]  \[
y’=\frac{x2}{x^24x+3}, y(0)=2;
\]
 \[
 Find with precision 5%
\[
\int_{\pi}^\pi\cos(x)^{100} dx.
\](hint a: \(\cos(x)=(e^{ix}+e^{ix})/2\); hint b: \(\cos(x)\approx 1x^2/2\) for small \(x\)).
class of 8.29
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