sin a=7/25, a lies in quadrant ii, and cos b=2/5, b lies in quadrant i find cos(a-b)

Question

Use the given information to find the exact value of the expression.

Answer 1

sin a = 7/25 7-24-25 right triangle: Therefore, cos a = -24/25 (2nd Quadrant - cos < 0

cos b = 2/5 2 is one leg, hyp is 5, other leg is sqrt(5²-2²) = sqrt(21) sin(b) = sqrt(21)/5

cos(a-b) = cos(a)cos(b) + sin(a)sin(b) = (-24/25)(2/5) + (7/25)(sqrt(21)/5) = (-48+7sqrt(21))/125 = -.1274

Checked: 163.74, 66.42 are a and b and .1274 is the cos(97.32)

Hope that helps.