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

Accepted Answer

Welcome back everyone. In this video, we want to determine the coordinates of the point on the plane curve represented by the parametric equations. X equals 11 plus seven multiplied by the cosine of U and Y equals 13 plus five multiplied by the sine of U where U is equal to pi for our answer choices A is the card in it. 4, 13, B is 18, 13, C is 4, 18 and D is 13 4. Now, what do we already know? Well, we know that these equations are parametric and that just means it's a fancy way for us to draw some really exciting looking curves linked by one parameter. So on that curve, it means I'm just gonna draw something here that I think it probably would look like. And on that curve, then that point is related to the parameter U. So if we substitute U into our point, then we can figure out the values of X and Y. Now we know that U is equal to pi. So let's do that for both of them. So let's substitute U equals pi into X equals 11 plus seven multiplied by the cosine of you I'm going to call that equation one and Y equals 13 plus five multiplied by the sine of you. I'm going to call that equation two. So when I substitute it into equation one, X now becomes 11 plus seven multiplied by the cosine of pi. But what do we know about the cosine of pie? Well, the cosine of pi is negative one. So that means X is equal to 11 minus seven, which is equal to four. So X will be four if I substitute it into equation two, where Y equals 13 plus five multiplied by sine U that becomes 13 plus five, multiplied by the sign of pi and the sign of pi is equal to zero. So Y is going to be 13 plus zero. Oops not 10 0, which equals 13. Therefore, my X coordinate is four, my Y coordinate is 13, which means that my answer is a 4 13. Thanks for watching guys. 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 = 2 + 3 cos t, y = 4 + 2 sin t; t = π