Answer:
24/25
Step-by-step explanation:
P(u, v) = (3, 4) describes a triangle: One vertex is at the origin (0, 0) and the other at (3, 4). According to the Pythagorean Theorem, 3^2 + 4^2 = 5^2, so we know the hypotenuse length is 5 units.
Recall that the sine function is defined as opp/hyp, which here is 4/5, and that the cosine function as adj/hyp, which here is 3/5.
Finally, we'll apply the double angle formula sin 2x = 2 sinx cos x.
Substituting the values found above, sin 2x = 2(4/5)(3/5) = 24/25.
The sine of 2x (where x is the smaller acute angle whose vertex is (0, 0) ) is 24/25.
