Convert to Polar Coordinates (5,pi/3)

Problem

(5,π/3)

Solution

1. Identify the given coordinates. The problem provides a point in polar form (r,θ) where r=5 and θ=π/3

2. Apply the formula for the xcoordinate using x=r*cos(θ)

x=5*cos(π/3)

3. Evaluate the cosine function. Since cos(π/3)=1/2 we calculate the value.

x=5⋅1/2=2.5

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

y=5*sin(π/3)

5. Evaluate the sine function. Since sin(π/3)=√(,3)/2 we calculate the value.

y=5⋅√(,3)/2=(5√(,3))/2

Final Answer

(5,π/3)=(2.5,(5√(,3))/2)

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