If tanθ = 8/3 and cot ϕ = 5 /4, with θ and ϕ in the first quadrant, find the exact value of sin ( θ + ϕ ). Note: Be sure to enter EXACT values sin ( θ + ϕ ) =

Answer 1

Draw and label a diagram!

tan Θ = 8 / 3, then sin Θ = ?, cos Θ = ?

cot Φ = 5 / 4, then sin Φ = ?, cos Φ = ?

Now use appropriate sum formula

Answer 2

sin(θ + φ) = sinθcosφ + sinφcosθ;

cosθ = 1/√1 + 64/9 = 3/√73; sinθ = 8/√73

sinφ = 1/√1 + 25/16 = 4/√41; cosφ = 5/√41

sin(θ + φ) = 8/√73·5/√41 + 4/√41·3/√73 = 52/√2993