Verified answer

sin(π - t) = sin t = 4/5

sin(t + π) = -sin t = -4/5

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Reason: In a unit circle, sin(Θ) is the y coordinate. At the positions of t and π-t, you have the same y coordinate. At the positions of t and π+t, you have the opposite y coordinates. Or you can use double angle formula to verify it.

sin(A+B) = sinAcosB + cosAsinB

sin(π - t) = sinπcost - cosπsint = sint

sin(π + t) = sinπcost + cosπsint = -sint

It might help if you have the graph of sin sitting in front of you.

First, note that it is antisymmetric about y, e.g. sin is odd, and sin(-x) = -sin(x)

Then notice that if you shifted the the graph right by pi, eg sin(x) ---> sin(x-pi) (or left by pi, for that matter) that the new plot is just upside down, or -sin(x).

Using this knowledge, sin(pi - t) = -sin(t-pi) = sin(t)

and sin(t + pi) = -sin(t)