QUESTION 1The tangent ratio is the ratio of the length of the opposite side of the length of the adjacent side.From ΔVWX, [tex]\tan(X)=\frac{VW}{WX}[/tex]From ΔYZX, [tex]\tan(X)=\frac{YZ}{XZ}[/tex][tex]\therefore \tan(X)=\frac{VW}{WX}=\frac{YZ}{XZ}[/tex]QUESTION 2We use the tangent ratio to obtain;[tex]\tan(V)=\frac{Opposite}{Adacent}[/tex][tex]\tan(V)=\frac{WX}{VW}[/tex]QUESTION 3From ΔVWX, [tex]\tan(X)=\frac{VW}{WX}[/tex]We take the inverse tangent of both sides to obtain;[tex]X=\tan^{-1}(\frac{VW}{WX})[/tex][tex]\therefore \tan^{-1}(\frac{VW}{WX})=X[/tex]QUESTION 4From ΔVWX, [tex]\tan(V)=\frac{WX}{VW}[/tex]Taking the inverse tangent of both sides, we obtain;[tex]V=\tan^{-1}(\frac{WX}{VW})[/tex][tex]\therefore \tan^{-1}(\frac{WX}{VW})=V[/tex]QUESTION 5.We know that [tex]\tan(V)=\frac{WX}{VW}[/tex]and[tex]\tan(X)=\frac{VW}{WX}[/tex][tex](\tan X)(\tan V)=(\frac{VW}{WX})(\frac{WX}{VW}=1[/tex]QUESTION 6.[tex]\tan^{-1}(\frac{VW}{WX})=X[/tex][tex]\tan^{-1}(\frac{WX}{VW})=V[/tex]This implies that;[tex]\tan^{-1}(\frac{VW}{WX})+\tan^{-1}(\frac{WX}{VW})=X+V[/tex]QUESTION 7[tex]\tan 23\degree =0.4244[/tex]We round to the nearest 0.01 to obtain;[tex]\tan 23\degree =0.42[/tex]QUESTION 8[tex]\tan 43\degree =0.9325[/tex]We round to the nearest 0.01 to obtain;[tex]\tan 43\degree =0.92[/tex]QUESTION 9[tex]\tan ^{-1} 0.14=7.9696\degree[/tex]We round to the nearest 0.01 to obtain.[tex]\tan ^{-1} 0.14=7.97\degree[/tex]QUESTION 10[tex]\tan ^{-1} 1=45.00\degree[/tex]QUESTION 11[tex]\tan ^{-1} 0.14=7.97\degree[/tex]This implies that;[tex]\tan 7.97\degree=0.14[/tex]QUESTION 12[tex]\tan ^{-1} 1=45.00\degree[/tex]This implies that;[tex]\tan 45.00\degree=1[/tex]