Question

what are the cartesian coordinates of the point whose polar coordinates are (3, 150°) ?

Answer 1

Answer:

A polar coordinate

(

r

,

θ

)

in Cartesian coordinates is

(

r

cos

θ

,

r

sin

θ

)

Hence,

(

3

,

150

∘

)

in polar coordinate is

(

3

cos

150

∘

,

3

sin

150

∘

)

or

(

3

×

(

−

√

3

2

)

,

3

×

1

2

)

or

(

−

2.598

,

1.5

)

as Cartesian coordinates.

One can also draw an agle of

150

∘

on origin and trace the point

3

units on it.

graph{((x+(3sqrt3)/2)^2+(y-3/2)^2-0.005)(y+x/sqrt3)=0 [-5.188, 4.81, -2.18, 2.82]}

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Answer 2

The cartesian coordinates of the point is (-2.598,1.5).

Step-by-step explanation:

Given:

The point whose polar coordinates are (3, 150°).

To Find:

The cartesian coordinates of the point.

Solution:

As given-the point whose polar coordinates are (3, 150°).

$r=3 \ and \ \theta=150\textdegree$

Let the cartesian coordinates of the point is (x,y).

$x=r\ cos\theta$

   $=3\times cos150\textdegree$

   $=3\times (-\frac{\sqrt{3} }{2} )$

   $= -2.598$

$y=rsin\theta$

    $=3\times sin150\textdegree$

   $= 3\times \frac{1}{2}$

   $=1.5$

Thus,the cartesian coordinates of the point is (-2.598,1.5).

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