 In this video, we provide the solution to question number 12 from the practice final exam for math 1060 in which case we're asked to convert the polar coordinate 4 comma 11 pi over 6 into rectangular coordinates here. I should mention that this problem we've seen several times throughout the semester converting from polar coordinates to rectangular coordinates is similar to working with a complex number and its polar form or working with a vector either an algebraic or geometric representations. So if we're in polar coordinates here, this means that our radius is 4 and our angle here is 11 pi over 6. So the x coordinate is just going to be r cosine theta. So we end up with 4 times cosine of 11 pi 6, like so similar for the y coordinate. The y coordinate is going to be r sine theta. So we end up with 4 times sine of 11 pi 6, which we should mention 11 pi 6 references pi 6, but it's in the fourth quadrant. So cosine will be positive. So we get 4 cosine of pi 6 pi 6 is the same thing. Of course it's 30 degrees. But in the fourth quadrant, sine would be negative. So we get negative 4 sine of pi 6, like so at pi 6 or 30 degrees, sine gives us one half. So we get negative 4 over 2, which is negative 2. But cosine of pi 6 will give us root 3 over 2. So we end up with 2 root 3. And so our coordinates should be positive 2 times root 3, negative 2. And so we see the correct answer is in fact A.