SOLUTION: Sin a=-5/6 and cos B=11/15. If a is in Quadrant IV and B is in Quadrant I, find sin(a-b). Give an exact answer.

Question 617861: Sin a=-5/6 and cos B=11/15. If a is in Quadrant IV and B is in Quadrant I, find sin(a-b). Give an exact answer.
Answer by IFY(62) (Show Source): You can put this solution on YOUR website!

FIRST OF ALL WE START WITH SIN A = -5/6. IN WHICH ITS ON THE FOURTH QUADRANT.
COS A IS FOUND BY USING PYTHAGORAS THEOREM.
THEREFORE COS A = SQRT 11 / 6

SECONDLY WE GO WITH COS B = 11/15 . IN WHICH IT IS ON THE FIRST QUADRANT.
SIN B IS FOUND BY USING PYTHAGORAS THEOREM.
THEREFORE SIN B = SQRT 104 / 15.
WE FIND SIN( A - B ) USING THE SIN RULE.
SINA COSB - COSA SINB
- 5/6 * 11/15 - SQRT 11/6 * SQRT 104 /15
- 11/ 18 - SQRT 286 / 45
-55 - 2 SQRT 286 / 90

NOTE
SIN ( A + B) = SINA COS B + COSA SINB
COS (A + B) = COS A COS B + SIN A SINB
COS (A -B) = COS A COS B - SINA SIN B

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