SOLUTION: Given that sin A= -4/5 where A is in quadrant 3 and sin B= 12/13 where B is in quadrant 2. Find: A. cosA B. cosB C. sec(A-B) D. tan(2A) E. cos(B/2) Help!

Question 744624: Given that sin A= -4/5 where A is in quadrant 3 and sin B= 12/13 where B is in quadrant 2. Find:
A. cosA
B. cosB
C. sec(A-B)
D. tan(2A)
E. cos(B/2)
Help!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Given that sin A= -4/5 where A is in quadrant 3 and sin B= 12/13 where B is in quadrant 2. Find:
A. cosA=
..
B. cosB =
..
C. sec(A-B)=1/cos(A-B)
cos(A-B)=cosA cosB+SinA sinB=-3/5*-5/13+(-4/5)*12/13=15/65-48/65=-33/65
sec(A-B)=-65/33
..
D. tan(2A)=(2tanA)/(1-tan^2A)
tanA=sinA/cosA=(-4/5)/(-3/5)=4/3
tan(2A)=(8/3)/(1-16/9)=(8/3)/(-7/9)=-72/21
..
E. cos(B/2)==√((8/13)/2))=√(8/26)
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