Problem: Let r be the distance from the origin to a point P with coordinates x and y. Designate the ratio y/r by s and the ratio x/r by c. Then the values of s2βc2 are limited to the numbers:
Answer Choices:
A. less than -1 and greater than +1 , both excluded
B. less than -1 and greater than +1 , both included
C. between -1 and +1 , both excluded
D. between -1 and +1 , both included
E. -1 and +1 only
Solution:
s2βc2=r2y2βx2β
max. val. =r2y2β( when x=0)=11β=1
min. val. =r2βx2β( when y=0)=1β1β=β1
or
SinΞΈ=s Let s2βc2=β£aβ£
CosΞΈ=c Since s2+c2=1
2s2=1+β£aβ£;β£aβ£=2s2β1
Since max. value of s is 1,maxβ£aβ£=1