Question

Please answer quickly

Given: sin(A) = 4/5, pi/2 < A < pi and sin(B) = -2root5/5, pi < B < 3pi/2 What is the value of cos(A – B)?

Answer 1

-√5/5

Explanation:

Given the following

sin(A) = 4/5

sinB - -2√5/5

SinA = 4/5 = opp/hyp

We can get cosA

opposite = 4

hypotenuse = 5

Adj = √5²-4² (pythagoras theorem)

Adj = √25-16

Adj = √9

Adj = 3

Cos A = Adj/hyp

Cos A = 3/5

Also

Sin B = -2√5/5 = opp/hyp

opposite = -2√5

hypotenuse = 5

Adj = √5²-(2√5)² (pythagoras theorem)

Adj = √25-20

Adj = √5

Cos B = Adj/hyp

Cos B = √5/5

Evaluate cos (A-B)

cos (A-B) = cosAcosB + sinAsinB

cos (A-B) = 3/5(√5/5)+4/5(-2√5/5)

cos (A-B) = 3√5/25 - 8√5/25

cos (A-B) = -5√5/25

cos (A-B) = -√5/5

Hence the value of cos (A-B) is -√5/5