Question

Find the trigonometric ratios in standard position whose terminal arm passes through the points.
(iii) $\left(-24,-7\right)$

Answer 1

Let the terminal arm pass through the point C$\left(-24,-7\right)$.

$$\begin{gathered} \therefore x=-24\mathrm{and}y=-7 \\ \mathrm{Here},r=\sqrt{x^2+y^2}=\sqrt{(-24{)}^2+(-7{)}^2}=25 \\ \mathrm{Now},\mathrm{let}\mathrm{the}\mathrm{angle}\mathrm{be}\theta . \\ \therefore \sin \mathrm{\theta }=\frac{\mathrm{y}}{\mathrm{r}}=-\frac{7}{25};\mathrm{cosec}\mathrm{\theta }=\frac{\mathrm{r}}{\mathrm{y}}=-\frac{25}{7} \\ \cos \mathrm{\theta }=\frac{\mathrm{x}}{\mathrm{r}}=-\frac{24}{25};\sec \mathrm{\theta }=\frac{\mathrm{r}}{\mathrm{x}}=-\frac{25}{24} \\ \tan \mathrm{\theta }=\frac{\mathrm{y}}{\mathrm{x}}=\frac{7}{24};\cot \mathrm{\theta }=\frac{\mathrm{x}}{\mathrm{y}}=\frac{24}{7} \end{gathered}$$