\( 1 \leftarrow \) Choose the figure that shows an angle of \( \frac{5 \pi}{2} \) radians in standard position.

To choose the figure that shows an angle of \( \frac{5 \pi}{2} \) radians in standard position, we need to understand what this angle represents. In standard position, an angle is measured with its vertex at the origin of the coordinate plane, and its initial side along the positive x-axis. The angle is measured counterclockwise from the initial side. The full circle is \( 2\pi \) radians. Since \( \frac{5 \pi}{2} \) is greater than \( 2\pi \), we can subtract \( 2\pi \) from \( \frac{5 \pi}{2} \) to find the equivalent angle between \( 0 \) and \( 2\pi \). Let's calculate the equivalent angle: \[ \frac{5 \pi}{2} - 2\pi = \frac{5 \pi}{2} - \frac{4 \pi}{2} = \frac{\pi}{2} \] So, \( \frac{5 \pi}{2} \) radians is equivalent to \( \frac{\pi}{2} \) radians, which is a right angle. Here's what the standard position of \( \frac{\pi}{2} \) radians would look like: - The initial side is along the positive x-axis. - The terminal side is along the positive y-axis, forming a right angle with the initial side. If you have a set of figures to choose from, you would look for the one that shows a right angle in standard position, with the terminal side on the positive y-axis. This would be the correct figure for an angle of \( \frac{5 \pi}{2} \) radians.