sin(tan^(-1)(12/5)) Evaluate expression without using a calculator.

Answer 1

Let's call the angle whose tangent is 12/5 "x".
Then, we have:
tan(x) = 12/5

Let's assume that the opposite side of the triangle is 12 and the adjacent side is 5.

Using the Pythagorean theorem, we can find the hypotenuse:
h^2 = 5^2 + 12^2
h^2 = 25 + 144
h^2 = 169
h = 13

So, we have a right triangle with sides 5, 12, and 13.

Now, let's find the sine of the angle x.
sin(x) = opposite/hypotenuse
sin(x) = 12/13

Therefore, sin(tan^(-1)(12/5)) = sin(x) = 12/13.