Find the exact value of cosine left parenthesis alpha minus beta right parenthesis , given that sine alpha equals startfraction 35 over 37 endfraction and cosine beta equals five thirteenths , with alpha in quadrant ii and beta in quadrant iv.

-480/481

Step-by-step explanation:

In order to use the identity ...

cos (α-β) = cos (α) cos (β) + sin (α) sin (β)

we must find both sine and cosine of the given angles.

sin (α) = 35/37 and α is in quadrant II, so cos (α) = - √ (1 - (35/37) ^2) = - 12/37

cos (β) = 5/13 and β is in quadrant IV, so sin (β) = - √ (1 - (5/13) ^2) = - 12/13

Then the desired cosine is ...

cos (α-β) = (-12/37) (5/13) + (35/37) (-12/13) = - (12·5 + 35·12) / (37·13)

cos (α-β) = - 480/481