Given that sin α = −3/5 , where α is in the fourth quadrant, and cos β = −12/13 , where β is in the third quadrant, find the quadrant containing α + β.

Question

Please explain it with solutions so I can understand.

Answer 1

cosα = 4/5 and sinβ = - 5/13

cos(α + β) = cosαcosβ - sinαsinβ = 4/5(- 12/13) - (- 3/5)(- 5/13) = - 48/65 - 15/65 = - 63/65 < 0

sin(α + β) = sinαcosβ + cosαsinβ = - 12/13(- 3/5) + 4/5(- 5/13) = 16/65 > 0

So, (α + β) in 2nd quadrant

Answer 2

α = sin^-1 -3/5

α ≈ -36.86989765

β = cos^-1 -12/13

β ≈ 157.3801351