Trigonometry Help? (Double & Half Angle Formulas)

2. If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate sin 2 θ.

3. If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate cos 2 θ.

$\begin{array}{|rcll|} \hline r^2 &=& (4-r)^2+3^2 \\ r^2 &=& 4^2-8r+r^2+3^2 \\ 8r &=& 4^2+3^2 \\ 8r &=& 5^2 \\ r &=& \frac{5^2}{8} \\ r &=& \frac{25}{8} \\ \hline \end{array}$

2. If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate sin 2 θ.

$\begin{array}{|rcll|} \hline \sin(2\theta) &=& \frac{3}{r} \\ \sin(2\theta) &=& \frac{3}{\frac{25}{8}} \\ \sin(2\theta) &=& \frac{24}{25} \\ \hline \end{array}$

3. If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate cos 2 θ.

$\begin{array}{|rcll|} \hline \cos(2\theta) &=& \frac{4-r}{r} \\ \cos(2\theta) &=& \frac{4}{r}-1 \\ \cos(2\theta) &=& \frac{4\cdot 8}{25}-1 \\ \cos(2\theta) &=& \frac{32}{25}-1 \\ \cos(2\theta) &=& \frac{7}{25} \\ \hline \end{array}$