If \(\tan\theta = \dfrac{7}{24}\), find the values of all the other trigonometric ratios of θ (θ acute).

Answer: \(\sin\theta = \dfrac{7}{25}\), \(\cos\theta = \dfrac{24}{25}\), \(\cot\theta = \dfrac{24}{7}\), \(\sec\theta = \dfrac{25}{24}\), \(\operatorname{cosec}\theta = \dfrac{25}{7}\)

\(\cot\theta = \dfrac{1}{\tan\theta} = \dfrac{24}{7}\).

\(\sec^2\theta = 1 + \tan^2\theta = 1 + \dfrac{49}{576} = \dfrac{625}{576}\) \(\therefore \sec\theta = \dfrac{25}{24}\) and \(\cos\theta = \dfrac{24}{25}\).

\(\sin\theta = \tan\theta \times \cos\theta = \dfrac{7}{24} \times \dfrac{24}{25} = \dfrac{7}{25}\) and \(\operatorname{cosec}\theta = \dfrac{25}{7}\).