We can use the trigonometric identity:
tan(a) = sin(a) / cos(a)
We can rearrange this equation to solve for sin(a) and cos(a):
sin(a) = tan(a) * cos(a)
cos(a) = sin(a) / tan(a)
Given that tan(a) = -24/10, we can plug this into the above equations to find sin(a) and cos(a):
sin(a) = (-24/10) * cos(a)
cos(a) = sin(a) / (-24/10)
To solve for sin(a), we first need to find cos(a). Let's solve for cos(a) first:
cos(a) = sin(a) / (-24/10),
cos(a) = ( (-24/10) * cos(a)) / (-24/10),
10 * cos(a) = -24 * cos(a),
cos(a) = -24/10.
Now that we have found cos(a), we can use it to solve for sin(a):
sin(a) = (-24/10) * cos(a),
sin(a) = (-24/10) * (-24/10),
sin(a) = 576 / 100,
sin(a) = 5.76
So, sin(a) = 5.76/10 and cos(a)= -24/10.
