Find the polar coordinates for point P which has Cartesian coordinates
(1,-√3)
a) (1,5pi/6)
b) (1,5pi/3)
c) (√3,5pi/3)
d) (2,5pi/3)
x^2 + y^2 = r^2
tanθ = y/x
make sure you get the proper quadrant by checking the signs of x and y.
answer A?
(1,5pi/6)???
i refer you, again, to ... x^2 + y^2 = r^2
1^2 + (-√3)^2 = 1 + 3 = 4 = r^2
only one answer fits
To find the polar coordinates for a point given its Cartesian coordinates, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Let's calculate the polar coordinates for the point P(1, -√3).
Step 1: Calculate r
r = √(x^2 + y^2)
r = √(1^2 + (-√3)^2)
r = √(1 + 3)
r = √4
r = 2
Step 2: Calculate θ
θ = arctan(y/x)
θ = arctan((-√3)/1)
θ = arctan(-√3)
θ ≈ -π/3
However, θ is usually written in the range [0, 2π) for polar coordinates.
Adding 2π to θ will give the equivalent angle in the [0, 2π) range.
θ = -π/3 + 2π
θ ≈ 5π/3
Therefore, the polar coordinates for point P(1, -√3) are (2, 5π/3).
Comparing this result to the given options, the correct answer is (d) (2, 5π/3).