If tan θ = 7/2 and cot ϕ = 11/13, with θ and ϕ in the first quadrant, find the exact value of sin ( θ − ϕ ).

Answer 1

Draw and label diagrams!

tan θ = 7 / 2

sin θ = 7√51 / 51

cos θ = 2√51 / 51

cot φ = 11/ 13

sin φ = 13√290 / 290

cos φ = 11√290 / 290

sin (θ - φ) = (7√51 / 51)(11√290 / 290) - (13√290 / 290)( 2√51 / 51)