SOLUTION: Find cos(s + t) given that sin s = - square root of 3/3, with s in quadrant IV, and sin t= -square root of 5/6 with t in quadrant IV.

Algebra ->  Trigonometry-basics -> SOLUTION: Find cos(s + t) given that sin s = - square root of 3/3, with s in quadrant IV, and sin t= -square root of 5/6 with t in quadrant IV.      Log On


   

Question 1176583: Find cos(s + t) given that sin s = - square root of 3/3, with s in quadrant IV, and sin t= -square root of 5/6 with t in quadrant IV.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find+cos%28s+%2B+t%29+

given that

sin%28+s%29+=+-+sqrt%283%29%2F3, with s in quadrant IV
and sin+%28t%29=+-sqrt%28+5%29%2F6 with t in quadrant IV

if sin%28+s%29+=+-+sqrt%283%29%2F3-> opp%2Fhyp+=+-+sqrt%283%29%2F3

opp=-+sqrt%283%29
hyp=3
then
adj=sqrt%283%5E2-%28-+sqrt%283%29%29%5E2%29
adj=sqrt%289-3%29
adj=sqrt%286%29

then cos%28s%29=sqrt%286%29%2F3=sqrt%282%2F3%29 -> with s in quadrant IV, cos%28s%29 is > 0

if sin+%28t%29=+-sqrt%28+5%29%2F6-> opp%2Fhyp+=+-+sqrt%285%29%2F6
opp=-+sqrt%285%29
hyp=6
then
adj=sqrt%286%5E2-%28-+sqrt%285%29%29%5E2%29
adj=sqrt%2836-5%29
adj=sqrt%2831%29

then cos%28t%29=sqrt%2831%29%2F6 -> with t in quadrant IV, cos%28t%29 is > 0

+cos%28s+%2B+t%29+=cos%28s%29+cos%28t%29+-+sin%28s%29+sin%28t%29

+cos%28s+%2B+t%29+=sqrt%28186%29%2F18+-+sqrt%2815%29%2F18