Working with parametric equations Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation. x=−7cos⁡2t,y=−7sin⁡2t,0≤t≤π

Question

Working with parametric equations Consider the following parametric equations.  a. Eliminate the parameter to obtain an equation in x and y.  b. Describe the curve and indicate the positive orientation.  x=−7cos⁡2t,y=−7sin⁡2t,0≤t≤π

curwyrm · Accepted Answer

Step 1Given:The following parametric equations, x=−7cos⁡(2t),y=−7sin⁡(2t),0≤t≤π.Step 2a) To eliminate the parameter to obtain an equation in x and y.We have,The following parametric equations,x=−7cos⁡(2t)....(1)y=−7sin⁡(2t)....(2)Adding equations (1) and (2), we getx2+y2=(−7cos⁡(2t))2+(−7sin⁡(2t))2=49cos2(2t)+49sin2(2t)=49(cos2(2t)+sin2(2t))=49(1)….′By using trigonometricident ify}=49An equation in x and y is x2+y2=49.Step 3b) To describe the curve and indicate the positive orientation.We have,x2+y2=(7)2.The curve represents a circle at the origin, (0,0) and radius, r=7.To indicate the positive orientation, we will use the following parametric equations,x=−7cos⁡(2t),y=−7sin⁡(2t),0≤t≤π.The interval given is 0≤t≤π.Therefore, for t=0,x=−7cos⁡(2(0))=−7(cos⁡(0))=−7(1)=−7y=−7sin⁡(2(0))=−7sin⁡(0))=−7(0)=0.Implies the initial point is (−7,0).Fort=π,x=−7cos⁡(2π)=−7(1)=−7y=−7sin⁡(2π)=−7(0)=0Implies the end point is (−7,0).The initial point and the end point are equal, that is, (−7,0).Hence, the orientation is positive in anticlockwise direction.

Working with parametric equations Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation. x = -7 cos 2t, y = -7 sin 2t, 0 <= t <= pi

Answered question

Answer & Explanation

New Questions in Algebra II