ANSWER:
-7/25
STEP-BY-STEP EXPLANATION:
We can calculate the value of t, as follows:
[tex]\begin{gathered} \sin t=\frac{4}{5} \\ t=\arcsin \mleft(\frac{4}{5}\mright) \\ t=53.13\text{\degree} \end{gathered}[/tex]Now, we calculate the cosine of 2t, like this:
[tex]\begin{gathered} \cos (2\cdot53.13) \\ \cos (106.26)=-0.28=-\frac{7}{25} \end{gathered}[/tex]