Question

if
x= a tan^2 theta
when x= 0, then theta=?
and
when x= a, then theta=?

Answer 1

when x= 0
\(0= a \tan^2 \theta \\ 0=\tan \theta\)
for what value of theta is tan theta =0 ???

Answer 2

it means
when x= 0, then theta=0

Answer 3

correct :)
when x=a
\(a= a \tan^2 \theta \\ 1=\tan \theta\)
for what value of theta is tan theta =1 ???

Answer 4

pi/4

Answer 5

yes, pi/4 is correct.
is this problem related to integration ?

Answer 6

yup

Answer 7

oh, then ok.
otherwise, we have multiple values of theta when tan theta =0 or 1, but for integration purpose, what we did is sufficient.