Respuesta :
Answer:
Step-by-step explanation:
To write the trigonometric expression "sin(tan^-1 u)" as an algebraic expression in "u," we can use the relationship between sine and tangent functions in a right triangle.
1. Let's start by considering a right triangle with an angle whose tangent is u. This means that tanθ = u, where θ is the angle.
2. In this triangle, let's assign values to the sides such that the side opposite to angle θ is u, and the adjacent side is 1. This choice makes the tangent of the angle equal to the ratio of the opposite side to the adjacent side, which is u/1 = u.
3. Using the Pythagorean theorem, we can find the hypotenuse of the triangle. Since one side is 1 and the other is u, the hypotenuse h can be calculated as h = √(1 + u^2).
4. Now, we can find the sine of angle θ using the opposite side and the hypotenuse: sinθ = opposite/hypotenuse = u/√(1 + u^2).
5. Therefore, sin(tan^-1 u) can be expressed as sinθ, which is u/√(1 + u^2). This is the algebraic expression in terms of u for the trigonometric expression sin(tan^-1 u).
By following these steps, you can understand how to convert the given trigonometric expression into an algebraic expression involving u.
