If we know that sin(t) = 5/7 , how to find other identies like cos(t) and tan(t) ?

Given that sin(t) = 5/7, we need to find cos(x) and
tan(x)

We will use trigonometric identities to find
cos(x)

We know that sin^2 x + cos^2 x =
1

==> cosx = +-sqrt(1-sin^2
x)

Let us substitute with sinx =
5/7

==> cosx = +-sqrt(1-
(5/7)^2]

                = +-
sqrt(1-25/49)

                =
+-sqrt(24/49)

                = +-2sqrt6/
7

Then cosx = +- 2sqrt6 /
7

Now we know that tanx =
sinx/cosx

==> tanx = (5/7) / (+-2sqrt6 /
7)

                = +-
5/2sqrt6

               = +-5sqrt6/
12

==> tanx= +-5sqrt6 /
12