In Exercises 1–8, parametric equations and a value for the parame...

Question

In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

x = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2

Accepted Answer

Welcome back everyone. In this problem, we want to determine the coordinates of the point on the plane curve represented by the parametric equations. X equals seven plus four, multiplied by the cosine of U and Y equals eight plus 11 multiplied by the sine of U where U is equal to half of pi for our answer choices A is the coordinate 11 19, B is 78, C is 19 7 and D is 7 19. Now, what do we already know? We know that this is a parametric equation. So it's a way to link two variables to make some fancy curve. And those two curves are related by that common parameter. U. So we can find the para, we can find the points by substituting the value of U into both equations. So I'm going to call X equals seven plus four multiplied by the cosine U equation one. And I'm going to call Y equals ele eight plus 11 multiplied by the sign of U as equation two. So in equation one, solving for Y or sorry, solving for X, solving for X in equation one, then X is going to be equal to seven plus four multiplied by the cosine of U which is half of pi, not the cosine of a half of pi. That would just be equal to zero and four multiplied by 00. Therefore, X equals seven. Next solving for why? OK. In equation two, that means Y equals eight plus multiplied by the sign of you. So the sign of a half of pi now the sign of a half of pi is one. So that will be eight plus 11 multiplied by one which is 19. Therefore, our XRN it is seven, our Y value is 19, which means that our solution is answer choice. D Thanks a lot for watching. I hope this video helped.

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In Exercises 1–8, parametric equations and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = 4 + 2 cos t, y = 3 + 5 sin t; t = π/2