introduction to mathematical reasoning lecture 6
TRANSCRIPT
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7/26/2019 Introduction to Mathematical Reasoning Lecture 6
1/3
:
ture6
Example
=-3
-
Si
Convert
o
polar
form
z=r(
cosotisinotrciso
ring
--HPtfs5M=My
a-
aretantta
)
-
arctanl
S
)
returns
avalue
between
-
%andTY2
-
counterclockwise
0=1.03
so
,
-3
-
5i=34h'
cis
(4.17)
-5
.
-
in
our
case
,
not
unique
cis(
4.17+2
't
'
)
-3
1.03
F
,
)
,
}
A-
1.03+7=4.17
If
K=
-1
,
OR
-3
-
Si
.
.
Mc
;s(
-2.11
)
youget
-
clockwise
-
.
-
-5
Example
mpvlethepo1arformof3-3ir-fEH-T-3M2oarctanHH.Ft2tkWhyPo1a3-3i-3M2.cisfTYtt2tHZi-rilcos9tisinAi3Zz-rzkosO2tisinOd1.Ie.3.4Z.5krolcos9tisinAHcoso2tisinod-rir2.cosQcosos-sino.sinoDComputingPoTlRktilsin.osinsotcosacosoDDefinitioniei0-cosotisino@tampabay
,+q
)
.
irrational
z
,
Tryo
:#
number
ei
"=
costtisint
.
-1.10=-1
o
,+
iZ2
oe#H=O
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7/26/2019 Introduction to Mathematical Reasoning Lecture 6
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Homework
.im#=29t+3ft=3Fe=Ef
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7/26/2019 Introduction to Mathematical Reasoning Lecture 6
3/3
xample
=1
,
z=
?
x3=1
x=3M=/
This
istheonlyreal
solution
z=P
.
c
;s(5
Angle
-3=0
(
osA=CosB
\
Too
Zrcisa
.
?
23=1
A=B2tK