If tan θ = $\dfrac{8}{15}$, find the values of other trigonometrical ratios for θ.

tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{8}{15}$

Let perpendicular = 8x and base = 15x

By pythagoras theorem, we get :

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = (15x)² + (8x)²

Hypotenuse² = 225x² + 64x²

Hypotenuse² = 289x²

Hypotenuse = $\sqrt{289x^2}$

Hypotenuse = 17x

Now, calculating the remaining trigonometric ratios :

sin θ = $\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{8x}{17x} = \dfrac{8}{17}$.

cos θ = $\dfrac{\text{Base}}{\text{Hypotenuse}} = \dfrac{15x}{17x} = \dfrac{15}{17}$

cot θ = $\dfrac{\text{Base}}{\text{Perpendicular}} = \dfrac{15x}{8x} = \dfrac{15}{8}$

sec θ = $\dfrac{\text{Hypotenuse}}{\text{Base}} = \dfrac{17x}{15x}= \dfrac{17}{15}$

cosec θ = $\dfrac{\text{Hypotenuse}}{\text{Perpendicular}} = \dfrac{17x}{8x} = \dfrac{17}{8}$