if sin s = -5 /13

Question

and sin t -3/5

s is in QIII
t is in QIV

find tan (s-t)

i got that tan (s-t)= 56/53

is that right? can someone check my work?

Answer 1

If sin s = -5/13, and it is in the third quadrant, cos s = -12/13
s = 202.620 degrees

If sin t is -3/5, and t is in the fourth quadrant, cos t = 4/5.
t = 323.130 degrees

tan (s-t) = sin (s-t)/cos(s-t)
= [sin s cos t - sin t cos s]/
[cos s cos t + sin s sin t]

Crunch the numbers. You should get a rational fraction, but your 53 in the denominator looks fishy.

You answer should be 56/33.