If tan θ = 12/5 and cot ϕ = 11/10, find the exact value of sin( θ + ϕ ).

Answer 1

If cot Φ = 11/10, tan Φ = 10/11

tan(Θ + Φ) = (12/5 + 10/11)/(1 - 12/5*10/11) = 182/55/(1 - 24/11) = -14/5

Then, sin(Θ + Φ) = ± 14/√(14²+(-5)²) = ±14/√221

Answer 2

tan θ = 12/5

= 2.4

θ=67.38°

cot ϕ = 11/10

cosΦ/sinΦ=1.1

Φ=42.25°

sin( θ + ϕ )

" (67.38+42.25)=

" 109.63=.9418.......°