SOLUTION: Find the tan(alpha-beta), if sin alpha=-5/13, cos beta=15/17, 3pie/2<alpha<2pie, and 0<beta<pie/2. So far I have cos alpha=12/13, and sin beta=8/17. I got stuck on how to even star

Algebra ->  Trigonometry-basics -> SOLUTION: Find the tan(alpha-beta), if sin alpha=-5/13, cos beta=15/17, 3pie/2<alpha<2pie, and 0<beta<pie/2. So far I have cos alpha=12/13, and sin beta=8/17. I got stuck on how to even star      Log On


   

Question 934380: Find the tan(alpha-beta), if sin alpha=-5/13, cos beta=15/17, 3pie/2 Please help! It will be greatly appreciated! Thank you
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the tan(alpha-beta), if sin alpha=-5/13, cos beta=15/17, 3pie/2 ***
reference angle a is in quadrant IV where sin<0, cos>0
sina=-5/13
cosa=12/13
tana=sin/cos=-5/12
..
reference angle b is in quadrant I where sin>0, cos>0
cosb=15/17
sinb=8/17
tanb=8/15
..
tan(a+b)=(tana+tanb)/(1-tana*tanb)
=(-5/12+8/15)/1-(-5/12)*8/15
=(-25/60+32/60)/(1+40/180)
=(7/60)/1+(2/9)=7/60/11/9=63/660
tan(a+b)=63/660