To find the terminal point (px, y) on the unit circle corresponding to the angle t = \frac{7\pi}{6}, we follow these steps:
1. Understanding the Unit Circle
The unit circle is a circle with a radius of 1 centered at the origin (0, 0) of a coordinate plane. Any point on the unit circle can be represented using the coordinates (x, y), where:
x = cos(t) and y = sin(t).
2. Finding the Angle in Degrees
First, it’s useful to recognize the angle in degrees. The angle \frac{7\pi}{6} radians equates to:
\frac{7\pi}{6} \times \frac{180}{\pi} = 210°
3. Location on the Unit Circle
The angle 210° is located in the third quadrant of the unit circle. In this quadrant, both the cosine (x-coordinate) and sine (y-coordinate) values are negative.
4. Calculating Cosine and Sine Values
To find the coordinates, we calculate:
cos(\frac{7\pi}{6}) = cos(210°) = -\frac{\sqrt{3}}{2}sin(\frac{7\pi}{6}) = sin(210°) = -\frac{1}{2}
5. Terminal Point (px, y)
Now, we can conclude that the terminal point (px, y) on the unit circle for the angle t = \frac{7\pi}{6} is:
(px, y) = \left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)
Summary
In summary, the coordinates of the terminal point on the unit circle for the given angle are:
Terminal Point: (px, y) = \left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)
This gives you the values corresponding to the angle on the unit circle.