# class of 8.29

• express $$\sin(3x)$$ in term of $$\sin(x)$$.
• express $$\cos(4x)$$ in terms of $$\cos(x)$$.
• simplify
$\sum_{k=-20}^{k=20} e^{k\phi}.$
1. solve

• $y’=\frac{2t}{1+t^2}, y(0)=0;$
• $y’=\frac{2t}{1-t^2}, y(0)=0;$
• $y’=\frac{2t}{1-t^2}, y(2)=0.$
2. solve
• $y’=\frac{2x^2-4x+3}{x-1}, y(0)=2;$
• $y’=\frac{x^2-4x+3}{x-2}, y(0)=2;$
• $y’=\frac{x-2}{x^2-4x+3}, y(0)=2;$
3. Find with precision 5%
$\int_{-\pi}^\pi\cos(x)^{100} dx.$

(hint a: $$\cos(x)=(e^{ix}+e^{-ix})/2$$; hint b: $$\cos(x)\approx 1-x^2/2$$ for small $$x$$).