Question

α and β are angles in standard position whose terminal sides lie in Quadrant II.If cosα = -24/25 and sinβ = 3/5, find cos(α - β).
-4/25
3/5
4/5
117/125

Answer 1

Answer:

The answer is 117/125

Step-by-step explanation:

The identity for the difference of 2 angles as far as cos goes is

cos(α-β) = cosα cosβ + sinα sinβ

We have both alpha and beta in QII.  In order to find the sinα, we need the missing leg, the one opposite the reference angle.  Applying Pythagorean's Theorem to that right triangle we get that the missing leg is +7 (y values are positive here so the 7 is positive since it is above the y = 0 line).  We also have to find the missing leg in beta so we can find the cosβ.  Applying Pythagorean's Theorem to that right triangle we get that the missing leg is -4 (negative because x is negative to the left of the origin).  Now that we have everything we need to fill in the identity, it looks like this:

$(-\frac{24}{25})(-\frac{4}{5})+(\frac{7}{25})(\frac{3}{5})$

Multiplying that out and then adding gives you

$\frac{96}{125}+\frac{21}{125}=\frac{117}{125}$