Use the given information to find a sinst btanst and c the q

Use the given information to find (a) sin(s+t), (b)tan(s+t) and (c) the quadrant of s+t.

coss=-8/17 and cost=-3/5, s and t are in quadrant III.

Thank you for your help!

Solution

cos s=-8/17

Therefore opposite= -15

sin s=-15/17

cos t=-3/5

that gives opposite=-4

sint=-4/5

sin(s+t)= sin s cos t+ cos s sint

= (-15/17)(-3/5)+(-8/17)(-4/5)= 77/85

cos(s+t)= (-8/17)(-3/5) -(-15/17)(-4/5)=84/85

tan(s+t)= sin(s+t)/cos(s+t)= 77/84