Answer:

Explanation:
In quadrant I of the Cartesian coordinate system, both the x-coordinate (cosine) and the y-coordinate (sine) of a point on the unit circle are positive. This means that if an angle θ is in quadrant I, then both sin θ and cos θ are positive.
Given sin θ = 12/13, we can calculate cos θ by using the trigonometric identity sin²θ + cos²θ = 1:

Since the tangent of an angle is defined as the ratio of sine to cosine (tan θ = sin θ / cos θ), and both sin θ and cos θ are positive in quadrant I, then tan θ is also positive in quadrant I.
Calculate tan θ by using the trigonometric ratio tan θ = sin θ / cos θ:

Finally, calculate tan 2θ using the Tangent Double Angle formula:

Therefore:
