If sin A = 3/5 and cos B = 24/25 and both angles a and b are in Quadrant I, what is the exact value of cos (A-B)
The choices are:
1) 3/5
2) 4/5
3) 44/125
4) 117/125
I can't figure this out for the life of me
The choices are:
1) 3/5
2) 4/5
3) 44/125
4) 117/125
I can't figure this out for the life of me
-
sinA = 3 / 5
O / H = 3 / 5
O = 3
H = 5
A = √(5² - 3²)
A = √16
A = 4
cosA = A / H
cosA = 4 / 5
cosB = 24 / 25
A / H = 24 / 25
A = 24
H = 25
O = √(25² - 24²)
O = √49
O = 7
sinB = O / H
sinB = 7 / 25
cos(A - B) = cosAcosB + sinAsinB
cos(A - B) = (4 / 5)(24 / 25) + (3 / 5)(7 / 25)
cos(A - B) = 96 / 125 + 21 / 125
cos(A - B) = 117 / 125
O / H = 3 / 5
O = 3
H = 5
A = √(5² - 3²)
A = √16
A = 4
cosA = A / H
cosA = 4 / 5
cosB = 24 / 25
A / H = 24 / 25
A = 24
H = 25
O = √(25² - 24²)
O = √49
O = 7
sinB = O / H
sinB = 7 / 25
cos(A - B) = cosAcosB + sinAsinB
cos(A - B) = (4 / 5)(24 / 25) + (3 / 5)(7 / 25)
cos(A - B) = 96 / 125 + 21 / 125
cos(A - B) = 117 / 125