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 s2−c2 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:
s2−c2=r2y2−x2
max. val. =r2y2( when x=0)=11=1
min. val. =r2−x2( when y=0)=1−1=−1
or
Sinθ=s Let s2−c2=∣a∣
Cosθ=c Since s2+c2=1
2s2=1+∣a∣;∣a∣=2s2−1
Since max. value of s is 1,max∣a∣=1