Find (a) sin(α + β), (b) cos(α + β), and (c) the quadrant containing α + β.

Question

sin α = −3/5, α in the fourth quadrant; cos β = −12/13, β in the third quadrant

Answer 1

cos(a)=4/5, sin(b)=-5/13,,,,

minor correction in fractions

4/5*(-12/13)-(-3/5)(-5/13)=cos(a+b)<0 so a+b in Q2 or Q3 based on cos attributes

sin(a+b)=(-3/5)*(-12/13)+(-5/13)*4/5>0 so a+b in Q1 or Q2 based on sin

a+b in Q2 (or Q6, Q10, ...,), a+b certainly is more than 2π