PreCalculus
posted by Lucy on .
How do you work this problem. I cannot find an example in the book to illustrate how to work it.
Find the value of tan(ab) if cos a=3/5, sin b=5/13, 90<a<180, and 90<b<180
Thanks for any help

your text should have
tan(ab) = (tan a  tan b)/(1 + tanatanb)
so you will need tan a and tan b
cos a = 3/5 and a is in the second quadrant, so by sketching a diagram it is easy to see that sin a = 4/5 and
tan a =  4/3
similarly sin b = 5/13 and b is in quadrant II, so cos b = 12/13 and
tan b = 5/12
then tan(ab)
=(4/3  (5/12))/(1 + (4/3)(5/12))
= 33/56