sin(a) = 9/16 Assume a and angles in the first quadrant , with Determine cos(alpha + beta) and sin(beta) = 8/15

Question

sin(a) = 9/16 Assume a and angles in the first quadrant , with Determine cos(alpha + beta) and sin(beta) = 8/15

Answer 1

sina = 9/16 adjacent side = sqr(16^2 - 9^2) = sqr175 = 5sqr7

cosa = adjacent side over hypotenuse = 5sqr7/16

sinb = 8/15 cosb = sqr161/15 adjacent side = sqr(225-64) = sqr161

cos(a+b) cosacosb - sinasinb = (5sqr7)/16 x sqr161/15 - 9/16 x 8/15 = 5(7)sqr23/240 - 72/240 = (35sqr23 - 72)/240 = about 0.40

another check on the solution, or method for finding the cosine of a sum is:

use an inverse trig function on a calculator to find a and b

sina = 9/16 a = 34.228

sinb = 8/15 b = 32.231

a+b = 66.459

cos66.459 = 0.40