SOLUTION: simplify the given equation suppose that sec(a)=5/4 and tab(b)=-1, where 0<a<pi/2<b<pi. find cos(a+b)

Algebra ->  Linear-equations -> SOLUTION: simplify the given equation suppose that sec(a)=5/4 and tab(b)=-1, where 0<a<pi/2<b<pi. find cos(a+b)      Log On


   

Question 1163202: simplify the given equation
suppose that sec(a)=5/4 and tab(b)=-1, where 0
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


sec(a) = 5/4 and a in quadrant I means cos(a) = 4/5 and sin(a) = 3/5. Note this means angle a is a bit less than 45 degrees.

tan(b) = -1 and b in quadrant II means sin(b) = sqrt(2)/2 and cos(b) = -sqrt(2)/2. This angle is clearly 135 degrees.

Before we do actual calculations, note that the angle a+b is going to be a bit less than 180 degrees, which means cos(a+b) should be close to cos(180) = -1.



To 5 decimal places that is -.98995, which is indeed very close to -1.