For sin, cos, and tan, let's use an abbreviation.SOH-CAH-TOA[tex]sin=\frac{opposite}{hypotenuse}[/tex][tex]cos=\frac{adjacent}{hypotenuse}[/tex][tex]tan=\frac{opposite}{adjacent}[/tex]But before that, we should solve for the missing side.Since this triangle is a right triangle, we can use the Pythagorean Theorem.[tex]a^2+b^2=c^2 \\ \\ 6^2+8^2=c^2 \\ \\ c^2=36+64 \\ \\ c^2=100 \\ \\ c=10[/tex]So the hypotenuse is 10.Let's plug in.sin θ = 6/10 --> 3/5cos θ = 8/10 --> 4/5tan θ = 6/8 --> 3/4Now for the cosectant, secant, and cotangent, we'll just use the definitions.Cosectant is hypotenuse over opposite.Secant is hypotenuse over adjacent.Cotangent is adjacent over opposite.So they are basically the inverses.csc θ = 10/6 --> 5/3sec θ = 10/8 --> 5/4cot θ = 8/6 --> 4/3