more trigonometry...

[klt643]

Hello againnnn.
I've already solved this problem (i think), but I want to make sure my calculations are accurate. take a look:

If sin A = 3/5, O(less than or equal to) A (less than) pi/2, and cos B = -5/13, o (less than or equal to) B (less than) pi. Find the exact values of the following:
1. sin(A-B)
2. cos (A-B)
3. cos (B-A)

1. if sin A = 3/5, then cos A = 4/5. if sin B = 12/13 then cos b = -5/13
sin(a-b) = sinAcosB - sinBcosA
(3/5)(-5/13) - (12/13)(4/5)
answer: -63/65

2. cos(a-b) = cosAcosB + sinAsinB
(4/5)(-5/13) + (3/5)(12/13)
answer: 16/65

3. cos(b-a) = cosBcosA + sinBsinA
(-5/13)(4/5) + (12/13)(3/5)
answer: 16/65


thanks so much,
Katie

 

[tkhunny]

Good work.

Did you notice the Quadrant in which A-B and B-A live? Just an intereting thing to note.

The only thing I would improve is your notation. You switched back and forth between a, b, and A, B a time or two.