Question

Assuming
r > 0 and 0 ≤ θ < 2π,
the point P has polar coordinates
(r, θ) =

Answer 1

On a Cartesian plan & from the origin, draw a cercle &  a  radius(r)  that intersect  the cercle in P so that to form angle Ф, with the horizontal, then you will notice that the coordinate of P are rsinФ & rcosФ, which are the polar coordinate of P(rsinФ, rcosФ)

Answer 2

The polar coordinates are ( ±5√2,  7π/4)

What is Polar coordinates?

It is a two-dimensional coordinate system in which each point on a plane has a unique distance from a reference point and a specific angle from a reference direction.

By using polar coordinates we mark a point by how far away and at what angle it is.

To convert from rectangular coordinates to polar coordinates, use one or more of the formulas:  cosθ=xr, sinθ=yr, tanθ=yx, and r=√x2+y2.

As, point in the Cartesian plane is (-5 , 5)

r = √x² + y²

r = √[(5)² + (-5)²]

= √[25 + 25]

= √50

= ±5√2

Now,

θ = tan^-1 (y/x)

θ = tan^-1 (5/-5)

= tan^-1 (-1)

As, tan is negative in the II and IV quadrant

here, 0 ≤ θ < 2π

θ = 2π - tan^-1(1)

we know, in IV quadrant r > 0

θ = 2π - π/4 = 7π/4

Learn more about polar coordinates here:

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