How do you convert #(-2,-2)# into polar coordinates?

1 Answer
Jan 29, 2016

Answer:

The polar coordinates, in #(r, theta)# form, are #(sqrt8, -0.786)#. This is equivalent to #(sqrt8, (7pi)/4)#.

Explanation:

When converting from polar to rectangular coordinates, we can use:

#x = r cos theta#

#y = r sin theta#

Going in the opposite direction, our first step is to find #r#, the radius of the circle:

#r = sqrt(x^2 + y^2) = sqrt((-2^2)+(-2^2)) = sqrt8#

Now we know the radius, and this is the hypotenuse of a right-angled triangle with the other two sides being #x=-2# (adjacent) and #y=-2# (opposite). We can use the definition of trig functions to find the value of #theta#:

#sin theta = (opposite)/"hypotenuse" = -2/sqrt8#

Use your calculator, ensuring it is on radians rather than degrees mode, to find the angle whose sin is #-2/sqrt8: -0.786# #radians#.

This means that the polar coordinates, in #(r, theta)# form, are #(sqrt8, -0.786)#.

It's worth noting that this is equivalent to #(sqrt8, (7pi)/4)#.