Select your answer Convert \( 315^{\circ} \) into radians. \( \begin{array}{l}\frac{3 \pi}{4} \\ \frac{5 \pi}{5} \\ \frac{5 \pi}{6}\end{array} \) \( \frac{7 \pi}{4} \)

To convert degrees to radians, you can use the formula: radians = degrees × (π/180). So for \( 315^{\circ} \): \[ 315 \times \frac{\pi}{180} = \frac{315\pi}{180} = \frac{7\pi}{4}. \] Therefore, the correct answer is \( \frac{7 \pi}{4} \). Did you know that \( 315^\circ \) is located in the fourth quadrant of the unit circle? This means that the reference angle is \( 45^\circ \), or \( \frac{\pi}{4} \) radians. In this quadrant, the cosine value is positive while the sine value is negative, which gives \( \cos(315^\circ) = \frac{\sqrt{2}}{2} \) and \( \sin(315^\circ) = -\frac{\sqrt{2}}{2} \). When working with angles, it’s easy to mix up radians and degrees, especially in math problems. A common mistake is forgetting to multiply by \( \frac{\pi}{180} \) or mixing the two measures during calculations. To avoid such pitfalls, always double-check your angles and convert them consistently—using a calculator can help, or make a quick conversion chart for reference!