Question

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360° help please?

Answer 1

See if this diagram helps: the polar coordinates of (5, -5) are (r, θ).

Answer 2

would you mind explaining how to find polar coordinates please?

Answer 3

Sure. To find polar coordinates, you need to find the distance from the origin (r) and the angle at which the point is from the origin (θ).

First, to find r, you can use Pythagoras' theorem, since r is the hypotenuse of the triangle shown in the diagram.
\[r^2 = x^2 + y^2 \]\[r = \sqrt{x^2 + y^2}\]
From the coordinates, x = 5, y = -5. So:
\[r = \sqrt{5^2 + (-5)^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2}\]
For this particular question, it's better to find the angle inside the triangle, then subtract it from 360 degrees.

\[\tan(a) = \frac{ y }{ x } \]\[a = \tan^{-1} (\frac{ 5 }{5 }) = \tan^{-1}(1) = 45 \]\[\theta = 360 - a = 360 - 45 = 315\]
So the polar coordinates are (5√2, 315°).

Answer 4

Sorry for the lengthy answer!

Answer 5

thank you so much! for all the help!