Question

Using a Difference Identity to Find an Exact Value. Find the exact value of cos(a – B) given sin(a) = -4/5 and cos (B) = -5/8 - for a in Quadrant III and B in Quadrant II.

Answer 1

To find the exact value of cos(a - B), use the difference identity for cosine and plug in the given values. The exact value is 7/20.

Step-by-step explanation:

To find the exact value of cos(a - B), we can use the difference identity for cosine. The difference identity states that cos(a - B) = cos(a)cos(B) + sin(a)sin(B). In this case, sin(a) is given as -4/5 and cos(B) as -5/8. Since a is in Quadrant III and B is in Quadrant II, sin(a) and cos(B) are negative. Plugging in the values, we get:

cos(a - B) = (-4/5)(-5/8) + (3/5)(4/5) = 1/4 + 12/25 = 7/20

To find the exact value of cos(a − B), we use the cosine difference identity. By determining cos(a) and sin(B) using given values and the Pythagorean identity, and then applying the identity cos(a − B) = cos a × cos B + sin a × sin B, we obtain an exact value of 3(5 - 4√{13})/40.