SOLUTION: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β) and cos(α - β)

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Question 1032545: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β) and cos(α - β)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β) and cos(α - β)
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Use the formulas 

 =     (1)

   and

 = .   (2)


Regarding these formulas, see the lesson Addition and subtraction formulas in this site.


In addition to the given   =   and   = , you need to know   and .


1.   =  =  =  =  =  = + = .

   The sign "+" was chosen for the square root because  is in Q1.


2.   = =  =  =  =  =  = + = .

   The sign "+" was chosen for the square root because  is in Q2.


Now all you need to do is to substitute everything into formulas (1) and (2) and make the calculations.


 =  =  =  = ,   and

 =  =  =  = .


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β) and cos(α - β)
sin(α - β):

cos(α - β):
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