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(b) The Cartesian coordinates of a suggest are (-2,3).(i) uncover polar coordinates (r,\theta) of the point, wherein r>0 and also 0 \le \theta r =\theta =(ii) find polar collaborates (r,\theta) the the point, whereby rr =\theta =

(b)

(i)

The Cartesian collaborates of a suggest (x,y) = (-2,3).

You are watching: The cartesian coordinates of a point are given.

x = -2 , y = 3

The Polar collaborates of a suggest (r,Θ) = ?

r = √ x² + y² )

r = √<(-2)² + 3²>

r = √(4+9)

r = √13

r = 3.62 > 0

Θ = 180 + tan-1(y/x) once x

Θ = 180 + tan-1(3/(-2))

Θ = 180 - 56.3099

Θ = 123.69°

0

Solution:

r = 3.62

Θ = 123.69°

(b)

(ii)

The Cartesian coordinates of a point (x,y) = (-2,3).

x = -2 , y = 3

The Polar coordinates of a point (r,Θ) = ?

r = √ x² + y² )

r = √<(-2)² + 3²>

r = √(4+9)

r = √13

r = ± 3.62

But the problem is r .

r = - 3.62

This is displayed in graph.

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Θ = 180 + tan-1(y/x) once x

Θ = 180 + tan-1(3/(-2))

Θ = 180 - 56.3099

Θ = 123.69°

As r is an adverse , edge slides 180° in anticlock wise direction.

Θ = 180° + 123.69°

Θ = 303.69°

0

Solution:

r = -3.62

Θ = 303.69°