SOLUTION: Information given: sin alpha=5/6, 90<alpha<180 and tan Beta=3/7, 180<Beta<270 what are cos(alpha+beta) sin(alpha+beta) and tan(alpha+beta)

Algebra ->  Trigonometry-basics -> SOLUTION: Information given: sin alpha=5/6, 90<alpha<180 and tan Beta=3/7, 180<Beta<270 what are cos(alpha+beta) sin(alpha+beta) and tan(alpha+beta)       Log On


   

Question 966322: Information given: sin alpha=5/6, 90 and tan Beta=3/7, 180 what are cos(alpha+beta) sin(alpha+beta) and tan(alpha+beta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Information given: sin alpha=5/6, 90 and tan Beta=3/7, 180 what are cos(alpha+beta) sin(alpha+beta) and tan(alpha+beta)
***
sin(a)=5/6 (Q2)

..
tan(b)=3/7(Q3)
hypotenuse of reference right triangle in quadrant III=sqrt%283%5E2%2B7%5E2%29=sqrt%289%2B49%29=sqrt%2858%29
sin%28b%29=-3%2Fsqrt%2858%29=-3sqrt%2858%29%2F58
cos%28b%29=-7%2Fsqrt%2858%29-7sqrt%2858%29%2F58
..
cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)=(-√11/6)(-7√58/58)-(5/6)(-3√58/58)=7√638/348+15√58/348=(7√638+15√58)/348
..
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)=(5/6)(-7√58/58)+(-√11/6)(-3√58/58)=-35√58/348+3√638/348=(-35√58+3√638)/348
..
tan(a+b)=sin(a+b)/cos(a+b)= (-35√58+3√638)/(7√638+15√58)/348
..
Check:
sin(a)=5/6(Q2)
a=123.56
tan(b)=3/7(Q3)
b=203.20
a+b=326.76
cos(a+b)=cos(326.76)=0.8364
exact value as computed above=(7√638+15√58)/348≈0.8363
sin(a+b)=sin(326.76)=-0.5481
exact value as computed above=(-35√58+3√638)/348≈-0.5482