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5.
(a) (10, 20)
c
:
√
√
500 ≈ 22.36
θ = atan2(20, 10) = arctan(20/10) ≈ 63.43
o
(10, 20)
c
r =
10
2
+ 20
2
=
100 + 400 =
∼
=
(22.36, 63.43
o
)
p
(b) (−12,−5)
c
:
√
169 = 13
θ = atan2(−5,−12) = arctan(5/12)−180
o
≈ 22.62
o
−180
o
≈−157.38
o
√
r =
(−12)
2
+ (−5)
2
=
144 + 25 =
∼
= (13,−157.38
o
)
p
(−12,−5)
c
(c) (0, 4.5)
c
:
0
2
+ 4.5
2
= 4.5
θ = atan2(0, 4.5) = 90
o
(4.5, 0)
c
≡ (4.5, 90
o
)
p
r =
(d) (−3, 4)
c
:
√
√
25 = 5
θ = atan2(4,−3) = arctan(4/3) + 180
o
≈−53.13
o
+ 180
o
≈ 126.87
o
(−3, 4)
c
≡ (5, 126.87
o
)
p
r =
(−3)
2
+ 4
2
=
9 + 16 =
(e) (0, 0)
c
≡ (0, 0)
p
(f) (−5280, 0)
c
(−5280)
2
+ 0
2
= 5280
θ = atan2(0,−5280) = 180
o
(−5280, 0)
c
≡ (5280, 180
o
)
p
r =
(a) x = r cos(θ) = 4 cos(120
o
) = 4(−1/2) = −2
y = r sin(θ) = 4 sin(120
o
) = 4(
6.
√
√
3
3/2) = 2
√
3, 5)
(b) x = r cos(θ) = 2 cos(45
o
) = 2(
so (x, y, z) = (−2, 2
√
2/2) =
√
2
√
√
2
y = r sin(θ) = 2 sin(45
o
) = 2(
2/2) =
√
2,
√
so (x, y, z) = (
2,−1)
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