QUESTION 1
The 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 2
We use the tangent ratio to obtain;
[tex]\tan(V)=\frac{Opposite}{Adacent}[/tex]
[tex]\tan(V)=\frac{WX}{VW}[/tex]
QUESTION 3
From 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 4
From 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]
