sin(\alpha + \beta ); sin \alpha = -(12)/(13) for \alpha in Quadrant IV; cos \beta = -(1)/(3) for \beta in Quadrant III

Answer 1

A= 360-67.38 = 292.62

A in Quad IV

B= 180+70.53 = 250.53

B in Quad III

A+B = 543.15

543.15 -360= 183.15

sin183.15 =-sin3.15 = about -.05

sinA = -12/13

A in Q4

cosA = 5/13

cosB = -1/3

B in Q3

sinB = -2sqr2/3

sin(A+B) = sinAcosB +sinBcosA

plug in the values

(-12/13)(-1/3) + ((-2sqr2)/3)(5/13)

= 12/39 - 10sqr2/39

= 12/39 - 10sqr2/(39)

=(12-14.14)/39

=-2.14/39

= about -.05

by either method

sin(A+B)= -0.05

rounded to one decimal place