Given:
The required angle is in the first quadrant with position P(u,v) = (3,4)
Let us begin by showing the position of the angle using the given position:
Using trigonometric ratios, we can solve for theta as shown:
[tex]\begin{gathered} \tan \text{ }\theta\text{ = }\frac{Opposite}{Adjacent} \\ \text{Substituting the given sides} \\ \tan \theta\text{ =}\frac{4}{3} \\ \theta\text{ = }\tan ^{-1}\frac{4}{3} \\ \theta=53.13^0 \end{gathered}[/tex]Solving for the required angle:
[tex]\begin{gathered} \tan (2\theta)\text{ =tan(2}\times53.13) \\ =tan106.26^0 \\ =\text{ -3.429} \end{gathered}[/tex]The result is equivalent to -24/7.
Answer: -24/7 (Option 3)
