Find the angle, in degrees between 0 and 360∘, which intersects the unit circle at the point (−√2/2,−√2/2).

The point \((- \sqrt{2}/2, - \sqrt{2}/2)\) on the unit circle is located in the third quadrant. This corresponds to an angle where both the sine and cosine values are negative.

For this point, both the x-coordinate (cosine) and the y-coordinate (sine) are equal to \(- \sqrt{2}/2\), which matches the reference angle of \(45^\circ\).

Since the point is in the third quadrant, we use the formula for finding the angle in this quadrant:
\[
\theta = 180^\circ + \text{reference angle}
\]

Thus, the angle is:
\[
\theta = 180^\circ + 45^\circ = 225^\circ
\]

Therefore, the angle that intersects the unit circle at the point \((- \sqrt{2}/2, - \sqrt{2}/2)\) is \(225^\circ\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the reference angle for a point in the fourth quadrant?
2. How can you determine which quadrant a point on the unit circle lies in?
3. What are the sine and cosine values for \(45^\circ\)?
4. How do we calculate angles for other quadrants using reference angles?
5. What are the coordinates of the point corresponding to \(315^\circ\)?

**Tip:** To find the angle based on coordinates on the unit circle, always identify the quadrant and the reference angle first.

Find the angle, in degrees between 0 and 360∘, which intersects the unit circle at the point (−√2/2,−√2/2).

Discover how to find the angle in the third quadrant that intersects the unit circle at the point (-√2/2, -√2/2). This problem covers key trigonometric concepts, including reference angles and quadrant-based angle calculations. Suitable for students in Grades 10-12.

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