Question

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.)

R lies between the circles x² + y² = 1 and x² + y² = 7 in the first quadrant

Answer 1

Ansker, Given Circles are xf y=1 q x+y=7 3. 2.6 Lconstant let u= Vartyr ve are tan (4/9) mity = 1 arty - 7 us Va't yr = 1 M artyr → o constant arctan (0/1)=0 V= arc tam (9(n) = are tan (Y/n = aretan (1/0) = 1/2 2.66 3 4 =1, u = F7, V=D and V = Now v= arctan (7/2) tanv=y al o constant 1.5 y = a tanu – Fartyr Now u= { Constant 015 = Tartartanu u= aittanu 2.4 3 4 u= a see v ( laten'v = sees) u= 즈 cos y .. n = u cov Now tan V = olt Y (:2=4 Colu) dan va u cov Y = ucorv. mv cosv y = 4 Smv. a=ucost and y= usmul Thank you,