sin(2arctan(12/5))
I always do these by drawing the triangle
$$let\:\theta = atan\:\frac{12}{5}$$
$$\\Sin(2 atan(12/5))\\=sin(2\theta)\\=2sin\theta cos\theta\\=2\times \frac{12}{13}\times \frac{5}{13}\\=\frac{120}{169}$$
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
