1. The problem is to understand how to apply reciprocal identities in trigonometry. 2. Reciprocal identities relate trigonometric functions to their reciprocals: $$\sin \theta = \frac{1}{\csc \theta}, \quad \csc \theta = \frac{1}{\sin \theta}$$ $$\cos \theta = \frac{1}{\sec \theta}, \quad \sec \theta = \frac{1}{\cos \theta}$$ $$\tan \theta = \frac{1}{\cot \theta}, \quad \cot \theta = \frac{1}{\tan \theta}$$ 3. To apply these identities, replace a trigonometric function with its reciprocal or vice versa when simplifying expressions or solving equations. 4. For example, if you have \( \frac{1}{\sin \theta} \), you can write it as \( \csc \theta \) using the reciprocal identity. 5. This helps especially when you want to rewrite expressions for easier manipulation or when given one function and needing to find the reciprocal function. 6. Always check the domain restrictions since some functions like \( \csc \theta \) are undefined where \( \sin \theta = 0 \). Final tip: Practice applying reciprocal identities by converting between functions to simplify or solve problems effectively.