Determine the angle t from the identity sin^2t=4/25 .

We'll verify if the given identity makes
sense.

We'll take square root both
sides:

sqrt [(sin t)^2] =
sqrt(4/25)

sin t = +2/5 or sin t =
-2/5

Since the values of the sine function belong to the range [-1 ;
1], the given identity makes sense.

We'll sove the 1st
case:

sin t = +2/5

t = (-1)^k*arcsin
(2/5) + k*pi

We'll solve the 2nd
case:

sin t = -2/5

angle
t = (-1)^(k+1)*arcsin (2/5) + k*pi