Evaluate the expression under the given conditions sinthetap

Evaluate the expression under the given conditions. sin(theta-phi); tan theta=5/12, theta in Quadrant III, sin phi=-squareroot 10/10, phi in Quadrant IV

Solution

tan = 5/12

sin=-5/[(5²+12²)] =-5/13

cos=-12/[(5²+12²)] =-12/13

sin =-(10)/10

cos =[10² -(10)²] /10 =90 /10

sin(-) =sincos -cossin

sin(-) =(-5/13)(90 /10) -(-12/13)(-(10)/10 )

sin(-) =(-590 - 1210)/130

sin(-) =(-1510 - 1210)/130

sin(-) =(-2710)/130