Question

Given the following polar coordinates give the Cartesian coordinate x. Note: r>0and0≤θ≤2π. Remember to consider the quadrant in which the given point is located when determiningθfor the point. (r , θ ) = ( 5.8 , 5.8 ) What is x?

Answer 1

x = + 5.136 units

Explanation:

This question pertains to the conversion of an arbitrary point (x,y) in Cartesian coordinate system to polar coordinate system denoted by (r,Q)

Given, a point A with polar coordinates ( 5.8 , 5.8 )

We are to compute the x coordinate of the point in Cartesian system:

We know that:

x = r*cos(Q)

Where , r is a coordinate of expression in polar coordinate giving magnitude of the position vector of any point. While Q is the angle made by the position vector with x-axis in radians. Hence,

x = 5.8 cos (5.8) = 5.136 units

To determine in which quadrant does x lies in:

Quadrant 1 : 0 < Q < pi / 2

Quadrant 2 : pi/2 < Q < pi

Quadrant 3 : pi < Q < 1.5 pi

Quadrant 4 : 1.5 pi < Q < 2pi

The given Q = 5.8 radians = 1.84 pi

Hence, we can see that it lies in 4th quadrant where 1.5 pi < Q < 2pi .

Hence the coordinate of x = + 5.136 units in Cartesian coordinate system.