Exercise 4.3.24. (a) Using de Moivre's formula for 23 where z = cis 0, find formulas for cos 30 and sin 30 in terms of cos 0 and sin 0. (*Hint*) (b) Using part (a), find a formula for cos 30 in terms of cos 0. (*Hint*) "There are other types of "morphisms" as well, such as homeomorphism (in topology), diffeomorphism (in differential topology), and just plain morphism (in category theory).
Exercise 4.3.24. (a) Using de Moivre's formula for 23 where z = cis 0, find formulas for cos 30 and sin 30 in terms of cos 0 and sin 0. (*Hint*) (b) Using part (a), find a formula for cos 30 in terms of cos 0. (*Hint*) "There are other types of "morphisms" as well, such as homeomorphism (in topology), diffeomorphism (in differential topology), and just plain morphism (in category theory).
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Exercise 4.3.24.
(a) Using de Moivre's formula for 23 where z = cis 0, find formulas for cos 30
and sin 30 in terms of cos 0 and sin 0. (*Hint*)
(b) Using part (a), find a formula for cos 30 in terms of cos 0. (*Hint*)
'There are other types of "morphisms" as well, such as homeomorphism (in topology).
diffeomorphism (in differential topology), and just plain morphism (in category theory).
60
CHAPTER 4 COMPLEX NUMBERS
(c) Show that for any n, it is always possible to find a formula for cos no in
terms of cos 0.
(d) * Show that for any even n, it is always possible to find a formula for
cos no in terms of even powers of cos 0.
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