How can you determine the terminal point (px, y) on the unit circle given the value of t = 3π/4?

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To find the terminal point (px, y) on the unit circle for the angle t = 3π/4, you can follow these steps:

  1. Understand the Unit Circle: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system. Any point on this circle can be described using coordinates (px, py) or in terms of trigonometric functions like cosine and sine.
  2. Convert the Angle: The angle t = 3π/4 radians can be converted to degrees if necessary. This angle is equivalent to 135°. It’s important to know that angles in standard position have their vertex at the origin, and the angle is measured counterclockwise.
  3. Find the Coordinates: On the unit circle, the coordinates of a point corresponding to an angle t are given by: (px, py) = (cos(t), sin(t)). For t = 3π/4:
    • px = cos(3π/4) = -√2/2
    • py = sin(3π/4) = √2/2
  4. Combine the Results: The terminal point corresponding to the angle 3π/4 on the unit circle would thus be:(px, py) = (-√2/2, √2/2).

Therefore, the terminal point (px, y) on the unit circle for the value of t 3π/4 is (-√2/2, √2/2).

This means if you go counterclockwise from the positive x-axis by an angle of 3π/4, you will find the terminal point at these coordinates, showcasing the beautiful symmetry of the unit circle!

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