Convert to Rectangular Coordinates (-5,(5pi)/2)

Problem

(−5,(5*π)/2)

Solution

1. Identify the polar coordinates (r,θ) from the given point, where r=−5 and θ=(5*π)/2

2. Simplify the angle θ by finding its coterminal equivalent within the interval [0,2*π)

(5*π)/2−2*π=(5*π)/2−(4*π)/2

θ=π/2

3. Apply the formula for the x-coordinate using x=r*cos(θ)

x=−5*cos(π/2)

x=−5*(0)

x=0

4. Apply the formula for the y-coordinate using y=r*sin(θ)

y=−5*sin(π/2)

y=−5*(1)

y=−5

Final Answer

(−5,(5*π)/2)=(0,−5)

Want more problems? Check here!