Use the information given below to find cos (α + β)

Question

Use the information given below to find cos (α + β).

sin α = 5/13, with α in quadrant I

tan β = 4/3, with β in quadrant III

Give the exact answer, not a decimal approximation.

cos(α + β ) = ?

Answer 1

You MUST draw a picture...

sin A = 5/13 and cos A = 12/13

sin B = -4/5 and cos B = -3/5 <--- sine and cosine are negative in quadrant 3

cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b)

= (12/13)*(-3/5) - (5/13)*(-4/5)

= -36/65 - (-20/65)

= -36/65 + 20/65

= -16/65