Coordenadas polares
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Transcript of Coordenadas polares
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Coordenadas PolaresCoordenadas Polares
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Coordenadas PolaresCoordenadas Polares
x
y
x
y
(x, y)
x
y
x
y
(x, y)
r
r
θθ
senry
rx
== cos
=
+=
x
yarctg
yxr
θ
22
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Coordenadas polaresCoordenadas polares
![Page 4: Coordenadas polares](https://reader036.fdocuments.es/reader036/viewer/2022071813/55a492c81a28ab9d7c8b4610/html5/thumbnails/4.jpg)
Una circunferenciaUna circunferencia
x
yr = 3; 0.000000 <= t <= 6.2831903=r
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Una rectaUna recta
x
y
τ=Π/6
6
πθ =
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1 2 3 4 5 6 7x
yr = 4sin(t); 0.000000 <= t <= 6.283190
Circunferencia dezplazadatsenr 4=
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Circunferencia dezplazadaCircunferencia dezplazada
1 2 3 4 5 6 7x
yr = 4cos(t); 0.000000 <= t <= 6.283190tr cos4=
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Una rosaUna rosar = 3cos(2t); 0.000000 <= t <= 6.283190tr 2cos3=
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Otra RosaOtra Rosa
1 2 3 4 5
tr 4cos3=
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1 2 3 4 5
RosasRosastr 3cos3=
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Más rosasMás rosastsenr 33=
1 2 3 4 5
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CircunferenciasCircunferencias
1 2 3 4 5
tr cos4=tr cos4−=
tsenr 4=
tsenr 4−=
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LemniscataLemniscata
tsenr 2322 =
1 2x
y
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CardiodeCardiodetr 3cos33+=
1 2 3 4 5 6 7
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CaracolasCaracolas
0,0
cos
cos
>>±=±=
ba
bar
bar
θθ
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RosasRosas
n pétalos si n es impar
2n pétalos si n es par
(n>1)
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Circunferencias y LemniscatasCircunferencias y Lemniscatas