sin(2arctan(12/5))

sin(2arctan(12/5))

I always do these by drawing the triangle

$$let\:\theta = atan\:\frac{12}{5}$$

sin(2arctan(12/5))

$$\\Sin(2 atan(12/5))\\ =sin(2\theta)\\ =2sin\theta cos\theta\\ =2\times \frac{12}{13}\times \frac{5}{13}\\ =\frac{120}{169}$$

Let's take the "arctan" part first....remember, this will return some angle

arctan(12/5) = 67.38013505196°

So.....2*arctan(12/5) = 2* 67.38013505196°   = 134.76027010392°

And...... sin( 134.76027010392°) = 0.710059171598