1
Phy 3221
Due: February 9, 2011
Homework set # 5
Note: If the problem is an even numbered one with answers in the back of the book,
then treat the problem as if you were asked to “show that” the answers in the back are
correct.
If you expect credit for your homework, then it is best to make it easily readable.
For these first few problems use the following identities that have been discussed in class:
eiθ = cos θ + i sin θ
(eiθ )∗ = e−iθ = 1/eiθ = cos θ − i sin θ
The star
∗
means “take the complex conjugate.”
Problem 1: Derive the following trig identity from the above equations:
Problem 2: Show that
Problem 3: Show that
cos2 θ + sin2 θ = 1
(1)
eiθ + e−iθ
cos θ =
2
(2)
eiθ − e−iθ
sin θ =
2i
(3)
Problem 4: Derive the following trig identity from the above equations:
d sin θ
= cos θ
dθ
(4)
Problem 5: Derive the following trig identity from the above equations:
d cos θ
= − sin θ
dθ
Textbook: Prob. 2-47
Textbook: Prob. 2-49
Textbook: Prob. 2-50
Textbook: Prob. 2-54
(5)