Question

Find the coordinates of the following points

Answer 1

If
(
a
,
b
)
is a are the coordinates of a point in Cartesian Plane,
u
is its magnitude and
α
is its angle then
(
a
,
b
)
in Polar Form is written as
(
u
,
α
)
.
Magnitude of a cartesian coordinates
(
a
,
b
)
is given by
√
a
2
+
b
2
and its angle is given by
tan
−
1
(
b
a
)
Let
r
be the magnitude of
(
−
2
,
5
)
and
θ
be its angle.
Magnitude of
(
−
2
,
5
)
=
√
(
−
2
)
2
+
5
2
=
√
4
+
25
=
√
29
=
r

Angle of
(
−
2
,
5
)
=
tan
−
1
(
5
−
2
)
=
tan
−
1
(
−
5
2
)
=
−
68.198
degree
⇒
Angle of
(
−
2
,
5
)
=
−
68.198
degree
But since the point is in second quadrant so we have to add
180
degree which will give us the angle.
⇒
Angle of
(
−
2
,
5
)
=
−
68.198
+
180
=
111.802
⇒
Angle of
(
−
2
,
5
)
=
111.802
=
θ
⇒
(
−
2
,
5
)
=
(
r
,
θ
)
=
(
√
29
,
111.802
)

⇒
(
−
2
,
5
)
=
(
√
29
,
111.802
)

Note that the angle is given in degree measure.