From euler’s relation eiθ = cosθ + isinθ,

(a) use series expansions to prove that cosθ = (eiθ+e-iθ)/2, and sinθ = (eiθ−e-iθ)/2i. (b) draw the appropriate diagrams to interpret these formulas geometrically.

Does the problem involve permutations or? combinations? do not solve. the matching section of an exam has 4 questions and 7 possible answers. in how many different ways can a student answer the 4 ? questions, if none of the answer choices can be? repeated?

An angle that measures between 90 and 180° is called a(,

How many of the 250 grandparents in the population would you expect to prefer online shopping with merchant a? merchant a: 4 merchant b: 6 merchant c: 2 merchant d: 3 other: 5 none: 5 answer choices: a.about 4 b.about 8 c.about 40 d.about 21