Question

If sin(x)=-12/13 and sec(x)=13/5, then what is sin(2x)?

Answer 1

being told that
\[\sec(x)=\frac{13}{5}\] is the same as being told that
\[\cos(x)=\frac{5}{13}\]
now use
\[\sin(2x)=2\sin(x)\cos(x)\] replacing
\[\sin(x)\] with
\[-\frac{12}{13}\]and
\[\cos(x)\] with
\[\frac{5}{13}\]