REDUCTION FORMUL A Reduce (simplify) the following trigonometric expression: \[ \tan \left(360^{\circ}+x\right) \] For example, the expression \( \sin \left(180^{\circ}+x\right) \) can be reduced to. \( \sin (x) \) INSTRUCTION: If you need to type a trigonometric function, put brackets around the angle. For example: \( \sin (x) \). Answer: \[ \tan \left(360^{\circ}+x\right)= \]

\[ \tan \left(360^{\circ}+x\right)=\tan (x) \] The tangent function has a periodicity of \(180^{\circ}\). This means that adding any multiple of \(360^{\circ}\) to the angle leaves the tangent value unchanged. So \( \tan \left(360^{\circ}+x\right) \) simplifies directly to \( \tan (x) \) since \(360^{\circ}\) is essentially a full rotation. Additionally, this periodic property makes working with trigonometric functions a lot easier! Whenever you encounter angles beyond \(360^{\circ}\) or even negative angles, you can always reduce them by adding or subtracting full rotations of \(360^{\circ}\) to find equivalent angles within the standard range. Happy simplifying!