Use the given information to find a sin s t b tan s t and

Use the given information to find (a) sin (s + t), (b) tan (s + t), and (c) the quadrant of s + t. cos s = 3/5 and sin t = -5/13, s and t in quadrant IV (a) sin (s + t) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

cos s = 3/5 ; sin t = -5/13

sin s = -4/5 ; cost = 12/13

a) sin(s+t) = sinscost+ cos s sint = (-4/5)(12/13) + (3/5)(-5/13)

= ( -48 -15)/ 65 = -63/65

b) cos(s +t) = cos s cost - sins sint = (3/5)(12/13) - (-4/5)(-5/13)

= 16/65

tan( s+t) = sin(s+t)/cos(s+t) = -63/16

c) sin(s +t) --- -ve

tan( s +t) --- -ve

So,(s +t) is in IVrt quadrant