Convert to Polar Coordinates (1, square root of 3)

Problem

(1,√(,3))

Solution

1. Identify the Cartesian coordinates (x,y) from the given point, where x=1 and y=√(,3)

2. Calculate the radius r using the formula r=√(,x2+y2)

r=√(,1+(√(,3))2)

r=√(,1+3)

r=√(,4)

r=2

3. Calculate the angle θ using the formula tan(θ)=y/x

tan(θ)=√(,3)/1

θ=arctan(√(,3))

4. Determine the quadrant to find the correct value of θ Since both x and y are positive, the point is in the first quadrant.

θ=π/3

5. Express the point in polar form (r,θ)

Final Answer

(1,√(,3))=(2,π/3)

Want more problems? Check here!