Final answer:
To find the value of sin (s t), substitute the given values of cos(s) and sin(t) into the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Calculate the final value to be sin(s t) = - 287/2197.
Step-by-step explanation:
To find the value of sin (s t), we can use the trigonometric identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Let's represent s t as a, where s = cos(a) and t = sin(a). Therefore, sin (s t) = sin(a). Given that cos(s) = -5/13 and sin(t) = 3/5, we can substitute these values into the identity to find the value of sin (s t). Using the identity, we have:
sin(s t) = sin(a) = sin(s)cos(t) + cos(s)sin(t) = sin(s)(3/5) + cos(s)(-5/13)
Now, substitute the values of cos(s) = -5/13 and sin(t) = 3/5 into the equation:
sin(s t) = (-5/13)(3/5) + (-5/13)(-5/13) = -15/65 + 25/169 = - 287/2197