Question

find the polar coordinates of the point whose cartesian coordinates are (3,3)​

Answer 1

Answer:

(  3 √ 2 , π / 4 ) .

Step-by-step explanation:

Given :

Cartesian coordinate ( 3 , 3 ) .

Here x=  3 and y = 3

For polar coordinate ( r , Ф )

r = √ ( x² + y² )

r = √ ( 9 + 9 )

r = 3 √ 2

Now :

Ф = tan⁻¹ ( y / x )

Ф = tan⁻¹ ( 3 / 3 )

Ф = tan⁻¹ ( 1 )

Ф = π / 4 .

Therefore , polar coordinate is (  3 √ 2 , π / 4 ) .

Answer 2

The polar coordinates of the point whose cartesian coordinates are (3,3) are $\bf \red{3\sqrt2 \angle 45^{\circ}}$

Given:

• Cartesian coordinates.
• (3,3)

To find:

• find the polar coordinates.

Solution:

Concept\formula: Polar coordinates are given by $r \angle \theta$

Where,

$\bf r = \sqrt{{x}^{2} + {y}^{2}}$

and

$\bf \theta = {tan}^{ - 1} \left( \frac{y}{x}\right)$

Step 1:

Find r from (x,y)=(3,3) with the help of formula.

$r = \sqrt{ {3}^{2} + {3}^{2} }$

or

$r = \sqrt{9 + 9}$

or

$r = \sqrt{18}$

or

$\bf r = 9 \sqrt{2}$

Step 2:

Find the angle.

$\theta = {tan}^{ - 1} \left( \frac{3}{3}\right )$

or

$\theta = {tan}^{ - 1}(1)$

or

$\bf \theta = 45^{ \circ}$

Thus,

Polar coordinates of point are $\bf 3\sqrt2 \angle 45^{\circ}$.

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