Sketch a unit circle and label the terminal points corresponding to t= pi/4, 3pi/4, 5pi/4, 7pi/4.

Include the coordinates of each point

To sketch a unit circle and label the terminal points corresponding to t = pi/4, 3pi/4, 5pi/4, and 7pi/4, follow these steps:

1. Start by drawing a circle with a radius of 1 unit. This circle represents the unit circle.

2. Mark the center of the circle as the origin (0, 0).

3. Divide the circle into four quadrants by drawing two perpendicular lines passing through the origin.

4. Label the positive x-axis as "x" and the positive y-axis as "y".

5. To find the terminal points, we need to locate the angles pi/4, 3pi/4, 5pi/4, and 7pi/4 on the unit circle.

- pi/4:
- Locate the angle pi/4 on the circle.
- Draw a line from the origin to the point where the angle intercepts the circle.
- The coordinates of this point are (sqrt(2)/2, sqrt(2)/2) or approximately (0.707, 0.707).

- 3pi/4:
- Locate the angle 3pi/4 on the circle.
- Draw a line from the origin to the point where the angle intercepts the circle.
- The coordinates of this point are (sqrt(2)/2, -sqrt(2)/2) or approximately (0.707, -0.707).

- 5pi/4:
- Locate the angle 5pi/4 on the circle.
- Draw a line from the origin to the point where the angle intercepts the circle.
- The coordinates of this point are (-sqrt(2)/2, -sqrt(2)/2) or approximately (-0.707, -0.707).

- 7pi/4:
- Locate the angle 7pi/4 on the circle.
- Draw a line from the origin to the point where the angle intercepts the circle.
- The coordinates of this point are (-sqrt(2)/2, sqrt(2)/2) or approximately (-0.707, 0.707).

6. Label each of the terminal points with their respective coordinates:
- t = pi/4: (sqrt(2)/2, sqrt(2)/2) or approximately (0.707, 0.707)
- t = 3pi/4: (sqrt(2)/2, -sqrt(2)/2) or approximately (0.707, -0.707)
- t = 5pi/4: (-sqrt(2)/2, -sqrt(2)/2) or approximately (-0.707, -0.707)
- t = 7pi/4: (-sqrt(2)/2, sqrt(2)/2) or approximately (-0.707, 0.707)

Remember, the unit circle has a radius of 1 unit, and the angles are measured counter-clockwise from the positive x-axis.

I am simply not going to do these. They are all virtually the same as the ones I already did for you.