Convert each of the following points from rectangular coordinates to polar coordinates.
(-1, 1)
A) (sqrt(2), pi/4)
B) (sqrt(2), 3pi/4)
C) (-sqrt(2), pi/4)
D) (-sqrt(2), 3pi/4)
E) None of These
the angle is in QII, so (B)
Generally, the radius is expressed as a positive number, though (-sqrt(2),-pi/4) would also have been correct.
To convert rectangular coordinates to polar coordinates, we use the formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
For each point (-1, 1), let's calculate the corresponding polar coordinates:
A) First, we calculate r:
r = √((-1)^2 + 1^2) = √(1 + 1) = √2
Next, we calculate θ:
θ = arctan(1/(-1)) = arctan(-1) = -π/4
Therefore, the polar coordinates for (-1, 1) are (√2, -π/4).
Now, let's calculate the polar coordinates for the remaining options:
B) r = √(2), θ = 3π/4
C) r = √(2), θ = π/4
D) r = √(2), θ = 3π/4
Since options B, C, and D have the same polar coordinates, all with r = √(2) and θ = 3π/4, we can combine them as (√2, 3π/4).
Therefore, the correct answer is E) None of These, as none of the options match the polar coordinates of (-1, 1).