3 Clarify formula. edit approved Jun 9 '17 at 15:29 datatype_void 10544 bronze badges You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn with the center on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcosx=r*cos θ and y=rsiny=r*sin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcosx=a+(r*cos θ) y=b+rsiny=b+(r*sin θ) Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn with the center on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcos θ and y=rsin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcos θ y=b+rsin θ Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn with the center on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=r*cos θ and y=r*sin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+(r*cos θ) y=b+(r*sin θ) Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r 2 clarify meaning edited Nov 19 '14 at 13:07 fer0x 24122 silver badges55 bronze badges You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn with the center on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcos θ and y=rsin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcos θ y=b+rsin θ Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcos θ and y=rsin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcos θ y=b+rsin θ Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn with the center on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcos θ and y=rsin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcos θ y=b+rsin θ Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r 1 answered Nov 19 '14 at 12:46 fer0x 24122 silver badges55 bronze badges You can use the parametric equation as marked by Krom. To understand why we used this formula you have to understand what the equation is. This equation is derived from the Parametric equation of circle. Considering the circle is drawn on the origin (O) as shown in the diagram below If we take a point "p" on the circumference of the circle, having a radius r. Let the angle made by OP (Origin to p) be θ. Let the distance of p from x-axis be y Let the distance of p from y-axis be x Using the above assumptions we get the triangle as shown below : Now we know that cos θ = base/hypotenuse and sin θ = perpendicular/hypotenuse which gives us cos θ = x/r and sin θ = y/r :: x=rcos θ and y=rsin θ But if the circle is not at the origin and rather at (a,b) then we can say that the center of the circle is shifted a units in x axis b units in y axis So for such a circle we can change the parametric equation accordingly by adding the shift on the x and y axis giving us the following equations : x=a+rcos θ y=b+rsin θ Where a & b are the x,y co-ordinates of the center of the circle. Hence we found x and y the co-ordinates of the point on the circumference of the circle with radius r