Question

If θ is a first quadrant angle in standard position with P(u,v) = (3,4) evaluate tan2θ1) 24/72) -8/73) -24/7

Answer 1

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:

`\begin{gathered} \tan \text{ }\theta\text{ = }(Opposite)/(Adjacent) \\ \text{Substituting the given sides} \\ \tan \theta\text{ =}(4)/(3) \\ \theta\text{ = }\tan ^(-1)(4)/(3) \\ \theta=53.13^0 \end{gathered}`

Solving for the required angle:

`\begin{gathered} \tan (2\theta)\text{ =tan(2}*53.13) \\ =tan106.26^0 \\ =\text{ -3.429} \end{gathered}`

The result is equivalent to -24/7.

Answer: -24/7 (Option 3)