SOLUTION: Given sin(alpha) = -8/9 and pi < alpha < 3pi/2 and sin(beta) = -7/8 and beta is in Quadrant III. Use sum and difference formulas to find Sin(alpha + beta) I've been stuck on thi

Algebra ->  Trigonometry-basics -> SOLUTION: Given sin(alpha) = -8/9 and pi < alpha < 3pi/2 and sin(beta) = -7/8 and beta is in Quadrant III. Use sum and difference formulas to find Sin(alpha + beta) I've been stuck on thi      Log On


   

Question 947064: Given sin(alpha) = -8/9 and pi < alpha < 3pi/2 and sin(beta) = -7/8 and beta is in Quadrant III. Use sum and difference formulas to find Sin(alpha + beta)
I've been stuck on this one for awhile and was hoping someone could help me out,
Thanks!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given sin(alpha) = -8/9 and pi < alpha < 3pi/2 and sin(beta) = -7/8 and beta is in Quadrant III. Use sum and difference formulas to find Sin(alpha + beta)
***
sina=-8/9
cosa=-√(1-sin^2(a))=-√(1-(64/81))=-√(17/81)=-√17/9
sinb=-7/8
cosb=-√(1-sin^2(b))=-√(1-(49/64))=-√(15/64)=-√15/8
...
sin(a+b)=sinacosb+cosasinb=-8/9*-√15/8+√17/9*-7/8=8√15/72+7√17/72=(8√15+7√17)/72
Check:
sina=-8/9 (Q3)
a≈242.73˚
sinb=-7/8 (Q3)
b≈241.04˚
a+b≈483.77˚
sin(a+b)≈sin(483.77)≈0.8312..
exact value:=(8√15+7√17)/72≈0.8312..