Question

suppose that sin alpha = -3/5 and cot Beta = -2/3. pi 14 years ago

Answer 1

if
\[\sin(\alpha)=-\frac{3}{5}\]then
\[\cos(\alpha)=-\frac{4}{5}\] by the 2-4-5 right triangle in your head.
\[\cos(2\alpha)=1-2\sin^2(\alpha)=1-2\times (\frac{3}{5})^2\]

Answer 2

i get

\[1-\frac{18}{25}=\frac{7}{25}\]

Answer 3

\[\cot(\beta)=-\frac{2}{3}\] means
\[\sin(\beta)=-\frac{3}{\sqrt{13}}\] and
\[\cos(\beta)=\frac{2}{\sqrt{5}}\]

Answer 4

then use
\[\sin(\alpha +\beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)\] by plugging in the numbers we found above

Answer 5

i.e.
\[-\frac{3}{5}\times\frac{2}{\sqrt{5}}+(-\frac{3}{\sqrt{13}})\times (-\frac{4}{5})\]