Question

Describe how you would find the maximum and minimum values for tangent of the typical angles used on the unit circle. What are these values?

Answer 1

3down votefavorite1Find minimum and maximum value of function f(x,y)=3x+4y+|x−y| on circle{(x,y):x2+y2=1}I used polar coordinate system. So I have x=cost and y=sint where t∈[0,2π).Then i exploited definition of absolute function and i got:h(t)={4cost+3sintt∈[0,π4]∪[54π,2π)2cost+5sintt∈(π4,54π)Hence i received following critical points (earlier i computed first derivative):cost=±45∨cost=±2√29Then i computed second derivative and after all i received that in (2√29,5√29) is maximum equal √29 and in (−45,−35) is minimum equal −235