From the figure (ii) given below, find the values of x and y in terms of t-ratios of θ.

From figure,

$\Rightarrow \text{cot θ} = \dfrac{\text{Base}}{\text{Perpendicular}} \\[1em] \Rightarrow \text{cot θ} = \dfrac{AB}{BC} \\[1em] \Rightarrow \text{cot θ} = \dfrac{x}{10} \\[1em] \Rightarrow x = 10 \text{ cot θ}. \\[1em] \Rightarrow \text{cosec θ} = \dfrac{\text{Hypotenuse}}{\text{Perpendicular}} \\[1em] \Rightarrow \text{cosec θ} = \dfrac{AC}{BC} \\[1em] \Rightarrow \text{cosec θ} = \dfrac{y}{10} \\[1em] \Rightarrow y = 10 \text{ cosec θ}.$

Hence, x = 10 cot θ and y = 10 cosec θ.