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Convert the rectangular coordinates (–6, 6) to polar coordinates.

Convert the rectangular coordinates (–6, 6) to polar coordinates.-example-1

2 Answers

1 vote

The polar coordinates are (6(
\sqrt[]{2}, 3pi/4).

Rectangular coordinates are in the form of (x, y) and Polar coordinates are expressed in the form of (r,
\theta).

Relation between polar coordinates and rectangular coordinates-

x = r cos(
\theta), y = r sin(
\theta) and x^2 +y^2 =r^2 ...(1)

So by using above formulas we can solve our question.

Here , x= -6 and y= 6

r^2 = (-6)^2 +(6)^2

=72

=>r = 6(
\sqrt[]{2})

Put the values of x and y in the mentioned formula in eq(1)

-6 = 6(
\sqrt[]{2} )cos
\theta

6 = 6(
\sqrt[]{2} )sin(
\theta),

=>-1/(
\sqrt[]{2} = cos(
\theta) , 1/
\sqrt[]{2}= sin
\theta

Here cos is negative and sin is positive so it lies in 2nd quadrant

so here
\theta lies between
(\pi)/(2) \leq\theta\leq\pi


\theta= π-π/4

=3π/4

So,(r,
\theta) = ( 6√2,
(3\pi)/(4) )

Convert the rectangular coordinates (–6, 6) to polar coordinates.-example-1
Convert the rectangular coordinates (–6, 6) to polar coordinates.-example-2
User Holyredbeard
by
8.3k points
5 votes

Answer: A Polar is (6√2,
(3\pi )/(4))

Explanation:

Draw a line to point (see image). You need to find the length of that line and then the angle. Polar(length, angle)

Using pythagorean theorem

length² = (6)² + (-6)²

length² = 36 +36

length =√72

length =
√(36 *2)

length = 6√2

To find angle:

The triangle size is 6-6-6√2 Let's proportionally shrink so we can use unit circle numbers to figure angle. Becomes: 1-1-√2

So when we do sin x = opp/adj

sin x =
(1)/(√(2) ) >get rid of radical on bottom

sin x =
(√(2) )/(2) > when is sin =
(√(2) )/(2) This happens at
(\pi )/(4) but we are in the 2nd quadrant so the angle is
(3\pi )/(4)

Polar is (6√2,
(3\pi )/(4))

Convert the rectangular coordinates (–6, 6) to polar coordinates.-example-1
User Shaqwan
by
8.3k points

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