2. Another key theorem is de Moivre's Theorem which states: (cos 0 + i sin 0)" = cos no + i sin ne. Use this theorem to prove the identity, cos 30 = 4 cos 0 -3 cos 0. Let n = 3. This identity is of particular importance in geometry as it plays a key part in proving what angles can be constructed using a compass and straightedge.
2. Another key theorem is de Moivre's Theorem which states: (cos 0 + i sin 0)" = cos no + i sin ne. Use this theorem to prove the identity, cos 30 = 4 cos 0 -3 cos 0. Let n = 3. This identity is of particular importance in geometry as it plays a key part in proving what angles can be constructed using a compass and straightedge.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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= cos 0 + i sin 0.
1. Determine the equation for Euler's Theorem when 0
= T. This is called Euler's Identity. In your own words, without the use of outside resources, make a
conjuncture about why this identity is often described as the most beautiful equation.
2. Another key theorem is de Moivre's Theorem which states:
(cos 0 + i sin 0)"
= cos no + i sin n0.
Use this theorem to prove the identity, cos 30 =4 cos 0 – 3 cos 0.
Let n = 3.
This identity is of particular importance in geometry as it plays a key part in proving what angles can be constructed using a compass and straightedge.
3. Verify the identity
cos(-x)
1+ sin(-x)
=2 sec x
1- sin(x)
cos(x)
Show all work and justify your steps.
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