What is the x-value at 150° ? Write as an exact value (no decimal).(1 point)

1 answer

To find the x-value (or cosine value) at 150°, we can use the unit circle.

At 150°, the coordinates of the point on the unit circle can be found as follows:

The angle 150° is in the second quadrant, and we can determine its reference angle:

\[ 150° - 90° = 60° \]

In the second quadrant, the cosine value (which gives the x-coordinate) is negative, while the sine value (y-coordinate) is positive. The cosine of 60° is \( \frac{1}{2} \). Therefore, the cosine of 150° would be:

\[ \cos(150°) = -\cos(60°) = -\frac{1}{2} \]

Thus, the x-value at 150° is:

\[ -\frac{1}{2} \]