Suppose 𝐴 is in Quadrant III and 𝐵 is in Quadrant IV. If sin(𝐴)=−7/25 and cos(𝐵)=63/65 , then cos(𝐴+𝐵) =

Answer 1

Using the double angle formula cos(a+b) = (cos a)(cos b) - (sin a)(sin b)

Have sin a = -7/25 so need to figure out cos a use Pythagorean theorem to get the the adjacent side which is -24 (we are in quadrant 3) so cos a = -24/25

you are given cos b = 63/65 Using the same technique and solving for the adjacent side we get sin b = -16/65(sin is negative in quadrant 4)

So now you have all 4 values and can substitute them in the formula

(-24/25)(63/65) - (-7/25)(-16/65)= -1512/1625 - 112/1625= 1624/1625

Answer 2

If sin(𝐴)=−7/25 and cos(𝐵)=63/65 , then cos(𝐴+𝐵) =?

cos(A) = sqrt(1 - sin^2(A)) so cos(A) = +-sqrt(1 - (-7/25)^2) = -0.96 because cos is negative in the 3rd quadrant. Similarly, sin(B) = +-sqrt(1 - (63/65)^2) = -0.2462 because sin is negative in the 4th quadrant.

now: cos(A + B) = cos(A)cos(B) - sin(A)sin(B) = -0.96x63/65 - (-7/25x-0.2462) = -1.0