### Problem StatementWhat is the smallest positive solution to \(5\sin^2 x - \cos^2 x = 1\)? Round to 2 decimal places.---### ExplanationThis problem involves solving a trigonometric equation to find the smallest positive solution for \(x\). The equation combines both sine and cosine functions, and solving it typically involves using trigonometric identities and algebraic manipulation.1. **Trigonometric Identity:** One key identity that might be useful is \(\sin^2 x + \cos^2 x = 1\).2. **Algebraic Manipulation:** You may try expressing the equation in terms of a single trigonometric function, using the identity mentioned above to simplify \(\cos^2 x\).3. **Potential Method of Solution:** - Substitute \(\cos^2 x\) with \(1 - \sin^2 x\). - Solve the resulting quadratic equation in terms of \(\sin x\). - Find the smallest positive solution for \(x\).This exercise is a practice of combining knowledge of trigonometry with algebraic techniques to find a specific numerical solution.

Name: ### Problem StatementWhat is the smallest positive solution to \(5\si
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: ### Problem StatementWhat is the smallest positive solution to \(5\sin^2 x - \cos^2 x = 1\)? Round to 2 decimal places.---### ExplanationThis problem involves solving a trigonometric equation to find the smallest positive solution for \(x\). The equ