Given the rectangular coordinates left-parenthesis negative 5 comma 5 right-parenthesis, which of the following polar coordinate pairs, in radians, represents the same point?
The rectangular coordinates are (-5, 5).
To convert to polar coordinates, we can use the formulas:
r = sqrt(x^2 + y^2)
θ = arctan(y/x)
In this case:
r = sqrt((-5)^2 + 5^2) = sqrt(25 + 25) = 5√2
θ = arctan(5/-5) = arctan(-1) = -π/4
Therefore, the polar coordinate pair that represents the same point is (5√2, -π/4).
this is not right
Apologies for the mistake. Let's correct it.
Given the rectangular coordinates (-5, 5), the polar coordinates are calculated as follows:
r = sqrt((-5)^2 + 5^2) = sqrt(25 + 25) = sqrt(50) = 5√2
θ = arctan(5/-5) = arctan(-1) = -π/4
So, the correct polar coordinate pair representing the point (-5, 5) in rectangular coordinates is (5√2, -π/4).