SOLUTION: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find cos(α - β).
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Question 1117290: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find cos(α - β).
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \sin\(\varphi\)\sin\(\psi\)\ +\ \cos\(\varphi\)\cos\(\psi\))
\ =\ \frac{4}{5})
and \ \in\ QI)
\ =\ \frac{16}{25}\ \Right\ \cos^2\(\alpha\)\ =\ 1\ -\ \frac{16}{25}\ =\ \frac{9}{25}\ \Right\ \cos\(\alpha\)\ =\ \pm\sqrt{\frac{9}{25}}\ =\ \pm\frac{3}{5})
But \ \geq\ 0)
for 
Hence \ =\ \frac{3}{5})
Similarly, and I leave the arithmetic to you:
\ =\ \frac{12}{13})
Therefore:
\ =\ \(\frac{4}{5}\)\(\frac{12}{13}\)\ +\ \(\frac{3}{5}\)\(-\frac{5}{13}\))
The rest is just arithmetic. Mind your signs.
John
My calculator said it, I believe it, that settles it
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