Solve for x r=8cos(x)

Problem

r=8*cos(x)

Solution

1. Identify the goal, which is to convert the polar equation r=8*cos(x) into a rectangular (Cartesian) equation using the standard conversion formulas.

2. Recall the relationships between polar and rectangular coordinates: x=r*cos(x) y=r*sin(x) and r2=x2+y2

3. Multiply both sides of the equation by r to create terms that are easily substituted.

r2=8*r*cos(x)

4. Substitute x2+y2 for r2 and x for r*cos(x)

x2+y2=8*x

5. Rearrange the equation by moving all terms to one side to prepare for completing the square.

x2−8*x+y2=0

6. Complete the square for the x terms by adding ((−8)/2)2=16 to both sides.

(x2−8*x+16)+y2=16

7. Simplify the expression into the standard form of a circle equation (x−h)2+(y−k)2=R2

(x−4)2+y2=16

Final Answer

r=8*cos(x)⇒(x−4)2+y2=16

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