Question

Find the trigonometric ratios in standard position whose terminal arm passes through the points.
(ii) $(5,-12)$

Answer 1

Let the terminal arm pass through the point B $(5,-12)$.

∴ $x=5\mathrm{and}y=-12$

$$\begin{gathered} \mathrm{Here},r=\sqrt{x^2+y^2}=\sqrt{5^2+(-12{)}^2}=13 \\ \mathrm{Now},\mathrm{let}\mathrm{the}\mathrm{angle}\mathrm{be}\mathrm{\theta }. \\ \therefore \sin \theta =\frac{y}{r}=-\frac{12}{13};\cos ec\theta =\frac{r}{y}=-\frac{13}{12} \\ \cos \theta =\frac{x}{r}=\frac{5}{13};sec\theta =\frac{r}{x}=\frac{13}{5} \\ \tan \theta =\frac{y}{x}=-\frac{12}{5};cot\theta =\frac{x}{y}=-\frac{5}{12} \end{gathered}$$