To find the terminal point (px, y) on the unit circle determined by a given value of t, we first need to understand the relationship between the angle t and the coordinates on the unit circle. The unit circle is centered at the origin (0, 0) with a radius of 1.
The angle t is typically measured in radians. For t = 6π, we can simplify this angle to find its equivalent position on the unit circle. Since the unit circle completes one full rotation (360 degrees or 2π radians) in a circle, we can reduce the angle modulo 2π:
Step 1: Simplifying t
To find the equivalent angle:
t = 6π mod 2π = 0This means that an angle of 6π is effectively the same as an angle of 0 radians.
Step 2: Determining the coordinates
Now, we can find the coordinates on the unit circle. For an angle of 0 radians, the coordinates (px, y) can be determined using the cosine and sine functions:
px = cos(0) = 1y = sin(0) = 0Thus, the terminal point (px, y) on the unit circle for t = 6π is:
(px, y) = (1, 0)Conclusion:
In summary, the terminal point on the unit circle for t = 6π is
(1, 0).