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

3

step-by-step explanation: