Final answer:
By constructing a right triangle with opposite side 3 and adjacent side 4, we find that the hypotenuse is 5. Hence, sin(tan⁻¹((3)/(4))) is the sine of the angle, which is 3/5.
Step-by-step explanation:
To evaluate sin(tan⁻¹((3)/(4))), we start by understanding that tan⁻¹((3)/(4)) gives us an angle whose tangent is 3/4. Recall that the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. By drawing a right triangle where the opposite side is 3 units and the adjacent side is 4 units, we can use the Pythagorean theorem to find the hypotenuse: √(3² + 4²) = √(9 + 16) = √25 = 5. Therefore, the sine of the angle is the opposite side over the hypotenuse, which in this case is 3/5.
Using this information, we conclude that sin(tan⁻¹((3)/(4))) = 3/5.