Suppose sina=4/5 and tanB=-3/4, where pi/2<a<B<pi. Find cot(a-B).

Answer 1

sinA = 4/5

tanB =-3/4

A and B are in quadrant II

reference angles are both 3-4-5 right triangles

cosA =-3/5

sinB = 3/5

cosB =-4/5

sin(A-B) = sinAcosB - cosAsinB = (4/5)(-4/5) - (-3/5)(-3/5) = -7/25

cos(A-B) = cosAcosB + sinAsinB = (-3/5)(-4/5)+(4/5)(3/5) = 24/25

cot(A-B) = 24/25 over -7/25 = 24/-7 = -3.42

to check, calculate A and B

A=126.87

B =143.13

A-B = -16.26

cot(-16.26) = -3.42

cot(A-B) = about -3.42