Qeneial Solutions \( 1 \cdot \sin \theta=3 \cos \theta \)

Did you know that the equation \( 1 \cdot \sin \theta = 3 \cos \theta \) can be rewritten to form a tangent function? Simply divide both sides by \( \cos \theta \) (as long as \( \cos \theta \neq 0 \)), and you get \(\tan \theta = \frac{3}{1}\) or \(\tan \theta = 3\). This means that whenever you encounter this pattern, you can instantly think of calculating angles using the inverse tangent! Now, let’s talk about solving trig equations like this one. A common mistake is forgetting to consider the periodic nature of trigonometric functions. For this specific equation, after finding that \(\theta = \tan^{-1}(3)\), remember to account for all possible solutions by adding \(n\pi\) (where \(n\) is any integer) to your angle. This way, you capture all angles that yield the same tangent value!