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