You are given that cos(A)=−3/5, with A in Quadrant II, and cos(B)=8/17, with B in Quadrant I. Find cos(A−B).

Answer 1

When we say cos(A) = −3/5, with A in Quadrant II, it denotes this:

where the height "4" was calculated from the Pythagorean Theorem. So we can write the sin(A) as 4/5

When we say cos(B) = 8/17, with B in Quadrant I, it denotes this:

where the height "15" was calculated from the Pythagorean Theorem. So we can write the sin(A) as 15/17

Using the angle subtraction equation: cos(A – B) = cos(A)cos(B) + sin(A)sin(B), plugging in the values we calculated, we get:

cos(A – B) = (-3/5)(8/17) + (4/5)(15/17)

cos(A – B) = -24/85 + 60/85 = 36/85

Answer 2

cos A = -3/5 → sin A = 4/5

cos B =8/17 → sin B = 15/17

cos (A - B) = cos A cos B + sin A sin B

Can you substitute values and answer?