Question 5(16pts). Consider the unit sphere S2:={(x,y,z)∈R3∣x2+y2+z2=1}, without the north pole N:=(0,0,1). One can make a 1−1 correspondence between podnts in the xN-plane (a,t)∈R2 and S2\(N) as follows: given a point (a,t,0) in the plane, draw the unique line that passes through the north pole N and the point (s,t,0). This line will intersect the sphere at some point (x,y1​z). 1. Find a parameteriaation of the sphere in term of these coordinates; in other words, find ⟨x(s,t),y(s,t),s(s,t)⟩. ii. Calculate the area element dA in this parameterization, and use it to calculate the surface area of the sphere.