SOLUTION: find the exact value of cos(a+B) if sin a= -4/5, and sin B= 5/13

Algebra.Com
Question 873142: find the exact value of cos(a+B)
if sin a= -4/5, and sin B= 5/13
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
find the exact value of cos(a+B)
if sin a= -4/5, and sin B= 5/13

cos(a) = ±√1-sinČ(a) =  =  =  =  = 

cos(B) = ±√1-sinČ(B) =  =  =  =  =  

Case 1:  a is in Q3 and B is in Q1

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (-3/5)(12/13) - (-4/5)(5/13) = -16/65

Case 2:  a is in Q3 and B is in Q2

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (-3/5)(-12/13) - (-4/5)(5/13) = 56/65

Case 3:  a is in Q4 and B is in Q1

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (3/5)(12/13) - (-4/5)(5/13) = 56/65

Case 4:  a is in Q4 and B is in Q2 

cos(a+B) = cos(a)cos(B) - sin(a)sin(B) = (3/5)(-12/13) - (-4/5)(5/13) = -16/65

Two possible solutions: -16/65 and 56/65

Edwin
RELATED QUESTIONS

Find the exact value of tan (a-b) if sin a= 4/5 and cos b = 5/13... (answered by solver91311)
find the exact value of cos(a+b) if sin a =4/5 and sin b= -5/13 ( - in 5 only)with a in... (answered by stanbon)
Find the exact value of tan (a + b) if cos a = -3/5, sin b = 5/13, 90° < a < 180°, and... (answered by robertb,ikleyn)
Find the exact value of sin(a-B) if sin a=(5/13) and sin B=(8/17) and a and B are between (answered by stanbon)
find the exact value of each. a. cos(theta)/2 if sin(theta)=12/13 and... (answered by Nate)
Angles A and B are located in the first quadrant. If sin A = 5/13 and cosB = 3/5,... (answered by Alan3354)
Find the exact value of sin(a+b), given that sin a=-4/5 and cos b = 12/13, with a in... (answered by ikleyn)
Find the value of tan(a-b) if cos a=4/5 sin b=-5/13 270 degrees < a < 360 degrees and 270 (answered by lwsshak3)
If cos(theta)=4/5, 0<(theta) (answered by lwsshak3)