S11_202Hhwk2

S11_202Hhwk2 - ECE 202H Spring 2011 Page 1 of 3 ECE 202H...

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Unformatted text preview: ECE 202H Spring 2011 Page 1 of 3 ECE 202H: Homework #2 Due: 27 January 2011 at 1:30 PM (5 Points) Questions that are marked with a circled asterisk ⊛ are to be submitted at the beginning of class on the specified due date. All other problems are provided for practice and are representative of problems that may be included on exams. Solutions to all problems will be posted after the due date. SHOW ALL WORK! Foundational Mathematics 1. ⊛ Derive the Taylor series expansion for the following functions: a. e x – commonly written exp(x) in engineering b. e jx , where = √− 1 c. cos x d. sin x e. e-jx 2. Use the Taylor series expansions of cos θ , sin θ and exp( θ ) to derive Euler’s relation: ¡ = cos ¢ + sin ¢ 3. Use Euler’s relation to derive the following relationships a. cos ¢ = 1 2 ¡ + £¡ ¤ b. sin ¢ = 1 2¡ ¡ − £¡ ¤ c. cos 2 ¢ = 1 2 (1 + cos2 ¢ ) d. sin( ¢ + ) = sin ¢ cos + cos ¢ sin 4. It is beneficial to be able to work with infinite (or at least seemingly so) series....
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S11_202Hhwk2 - ECE 202H Spring 2011 Page 1 of 3 ECE 202H...

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