Evaluate the expression under the given conditions. sin(θ − ϕ); tan(θ) = 3 4 , θ in Quadrant III, sin(ϕ) = − 3 10 10 , ϕ in Quadrant IV

Question

Please help with steps. I don't even know where to begin. Thank you :)

Answer 1

using x for θ and y for Φ

sin(x-y)=sinxcosy-cosxsiny

if tanx=3/4 then the hypotenuse is 5 because tan=opposite/adjacent

if siny=-3/10 then the other leg is √91 because sin=opposite/hypotenuse

sin(x-y)=(3/5)(√91/10)-(4/5)((-3/10)

sin(x-y)=3√91/50 + 6/25

sin(x-y)=3√91/50+12/50

sin(x-y)=(3√91+12)/50

Answer 2

Do you mind rewriting this out? I presume there's supposed to be some fractions in here, but just a bit confused given the way it turned out :) (I.e: I think '3 4' is supposed to be 3/4)