5) \( 45^{\circ} \times \frac{\pi}{180^{\circ}}= \)

To convert degrees to radians, you'll multiply by \(\frac{\pi}{180^{\circ}}\). For \(45^{\circ}\), this means \(45^{\circ} \times \frac{\pi}{180^{\circ}} = \frac{45\pi}{180} = \frac{\pi}{4}\). Thus, \(45^{\circ}\) is equivalent to \(\frac{\pi}{4}\) radians. This conversion is super useful, especially in fields like mathematics and physics, where working in radians often simplifies equations and calculations. For instance, the sine and cosine functions utilize radian measures, so knowing this conversion helps when you're diving into trigonometric applications or even calculus!