To sketch the angle $\theta = -\frac{7\pi}{4}$ in standard position, let’s break down the steps.

1. Convert the angle to positive form if needed: Since the angle is negative, we can add $2\pi$ to find an equivalent positive angle: $-\frac{7\pi}{4} + 2\pi = -\frac{7\pi}{4} + \frac{8\pi}{4} = \frac{\pi}{4}$ This means that $-\frac{7\pi}{4}$ is equivalent to $\frac{\pi}{4}$.

2. Locate $\frac{\pi}{4}$ on the unit circle: The angle $\frac{\pi}{4}$ is in the first quadrant, located 45° (or $\frac{\pi}{4}$ radians) counterclockwise from the positive x-axis.

3. Sketch the angle in standard position: Starting from the positive x-axis, move counterclockwise 45° (or $\frac{\pi}{4}$) to indicate the terminal side of the angle.

Following these steps will give you the correct position of the angle on the unit circle.

Would you like further explanation or have any questions on this?

Here are five related questions for practice:

1. How would you represent an angle of $-\frac{5\pi}{3}$ in standard position?
2. What quadrant would an angle of $\frac{3\pi}{4}$ fall into?
3. How do you determine the reference angle for $\theta = -\frac{7\pi}{4}$?
4. What are coterminal angles, and how do you find them?
5. How can you convert between degrees and radians?

Tip: Adding or subtracting $2\pi$ (or 360°) can help you convert between positive and negative angles while keeping the same terminal side.