Answer Happy

We are given the Cartesian coordinates (3,−3) and must convert this point to polar coordinates. Recall that to find polar coordinates (r,θ), we use the following equations. r2=x2+y2tan(θ)=xy​​ We can use these equations to find the following values for (x,y)=(3,−3). r2=x2+y2 =32+(2)2 =tan(θ)=xy​​ Step 2
Step 2 For the Cartesian coordinates (3,−3), we have found the following values for the equivalent polar coordinates. r2tan(θ)​=18=−1​ First, we wish to find polar coordinates with r>0. To find the positive value of r, we choose the positive square root to solve for r. We are also asked to find θ such that 0≤θ<2π. As (3,−3) is in the fourth quadrant, we choose a value of θ in the fourth quadrant with 0≤θ<2π such that tan(θ)=−1. θ= To finish, we find that polar coordinates of the given point with the required conditions are as follows. (r,θ)=(