You are given that cos(A)=−8/17, with A in Quadrant III, and cos(B)=20/29, with B in Quadrant I. Find cos(A+B). Give your answer as a fraction.

Answer 1

cos(A+B) = 155/493

angles A and B involve 8, 15, 17 and 20, 21, 27 right triangles

A in 3rd quadrant, B in 1st quadrant

cosA = -8/17, sinA = -15/17 15= sqr(17^2-8^2) = sqr(225) =15

cosB = 20/29 sinB = 21/29 21 = sqr(29^2 - 20^2) = sqr(441) = 21

cos(A+B) = cosAcosB - sinAsinB = (-8/17)(20/29) - (-15/17)(21/29) = -160/(17)(29) + (315)/(17)(29) =

=-155/493 = about 0.3144

cos(A+B) = 155/493 = about 0.3144

cosA = -8/17, A = 61.93+180 = 241.93 degrees

cosB = 20/29 B = 46.40

A+B = 241.93 + 46.40 = 288.32

cos288.32 = 0.3144