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2 cards from this section. Quick, good the night before a test.
Using Euler's identity, express cos(0) in terms of e^(ix).
Remember that e^(0) = 1.
What is the relationship between sin(x) and e^(ix)?
Focus on the difference of two exponentials.
What does Euler's identity express?
Think about the connection between different mathematical representations.
True or False: The sine function can be written as a difference of exponentials.
Review the definition of sine from a previous lecture.
Prove that e^(ix) + e^(-ix) = 2cos(x) using differentiation.
Use the properties of exponents and derivatives.
Using sin(x) = (e^(ix) - e^(-ix)) / (2i), find the integral of sin^2(x) from 0 to π.
Utilize the identity for sine to expand the expression before integrating.
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