Help plz!If A is a 3rd quadrant angle with tan A = 5/12 and b is a obtuse angle with sinB = 4/5 find cos(A-B)?

Question

Help plz!If A is a 3rd quadrant angle with tan A = 5/12 and b is a obtuse angle with sinB = 4/5 find cos(A-B)?

Answer 1

Angle A is in the third quadrant.

tanA = 5/12

sinA = -5/13

cosA = -12/13

Angle B is in the second quadrant.

sinB = 4/5

cosB = -3/5

cos(A - B) = (cosA)(cosB) + (sinA)(sinB)

cos(A - B) = (-12/13)(-3/5) + (-5/13)(4/5) = (36 - 20)/65 = 16/65

Answer 2

A = tan-1 (5/12) = 22.62 => 180+22.62=202.62

B = sin-1 (4/5) = 53.13 => 180-53.13=126.87

cos(202.62-126.87) = 0.246

Answer 3

Hey andor, Im sure using a calculator is not what the teacher wants so here is my way without a calculator.

Since A is in 3rd quadrant both sin A and cos A will be negative. So using Pythagereon Theroem (something like that) youll get Cos A

5^2 + 12^2 = 25 + 144 = 169 square root = 13

Cosine is Adjacent over Hypotenuse Cos A = -12/13 <negative 3rd quadrant

Now B angle you can use same Thereom. This time minus

5^2 - 4^2 = 25 - 16 = 9 square root = 3

Cos B = 3/5 now if its obtuse Cosine B should be negative if Im not mistaken

Cos [(-12/13) - (-3/5)] = Use algerbra and find common denominator and subtract. If Victor above is correct and you punch fraction into calculator you should get same answer unless Victor is wrong LOL

I hope thats right lol its been a while. Hoped that shed some light.