How do you evaluate the expression sin(u+v) given sinu=35 with π2<u<p and cosv=56 with π<v<3π2?

1 Answer
Dec 3, 2016

sin(u+v)=15+41136=0.0481

Explanation:

As sinu=35 and domain of u is given by π2<u<π i.e. u is in second quadrant and cosu is negative and

cosu=1(35)2=1925=1625=45

Further as cosv=56 with π<v<3π2, hence v is in third quadrant and sinv is negative and

sinv=1(56)2=12536=1136=116

Now sin(u+v)=sinucosv+cosusinv

= 35×(56)+(45)×(116)

= 1530+41130

= 15+41136

= 15+4×3.31736=1.73236=0.0481