[tex]\huge\red{Question}[/tex]
Find the polar coordinate of point whose Cartesian coordinates are (-1, -1)
[tex]\huge\green{Answer}[/tex]
the point lies in the third quadrant. ∴ the polar coordinates of the given point are ( 2 , 225 ∘ ) .
[tex]\huge ☘︎\bf \ \blue{Explaination}[/tex]
See the attachment
[tex]\small\pink{Hope \: it \: helps}[/tex]
Answer:
Here, x = - 1 and y = - 1
..the point lies in the third quadrant.
Let the polar coordinates be (r, 0)
r ^ 2 = x ^ 2 + y ^ 2 = (- 1) ^ 2 + (- 1) ^ 2 = 1 + 1 = 2
r = sqrt(2) ...[ r>0]
tane = y/x = - 1/- 1 = 1
Since the point lies in the third quadrant and 0 \le
theta < 2pi
tan theta = 1
= tan 45 deg
= tan(180 deg + 45 deg) ...I^ tane is periodic function
with period pi = 180 deg ]
tan theta = tan 225 deg
theta = 225 deg
..the polar coordinates of the given point are
(sqrt(2), 225 deg)
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[tex]\huge\red{Question}[/tex]
Find the polar coordinate of point whose Cartesian coordinates are (-1, -1)
[tex]\huge\green{Answer}[/tex]
the point lies in the third quadrant. ∴ the polar coordinates of the given point are ( 2 , 225 ∘ ) .
[tex]\huge ☘︎\bf \ \blue{Explaination}[/tex]
See the attachment
[tex]\small\pink{Hope \: it \: helps}[/tex]
Answer:
Here, x = - 1 and y = - 1
..the point lies in the third quadrant.
Let the polar coordinates be (r, 0)
r ^ 2 = x ^ 2 + y ^ 2 = (- 1) ^ 2 + (- 1) ^ 2 = 1 + 1 = 2
r = sqrt(2) ...[ r>0]
tane = y/x = - 1/- 1 = 1
Since the point lies in the third quadrant and 0 \le
theta < 2pi
tan theta = 1
= tan 45 deg
= tan(180 deg + 45 deg) ...I^ tane is periodic function
with period pi = 180 deg ]
tan theta = tan 225 deg
theta = 225 deg
..the polar coordinates of the given point are
(sqrt(2), 225 deg)