Math Problem Statement
Solution
The coordinates given in the problem are . These coordinates correspond to a point on the unit circle.
To determine the angle, we note that:
- is the -coordinate.
- is the -coordinate.
This point is in the fourth quadrant of the unit circle, where the cosine value (related to the -coordinate) is positive, and the sine value (related to the -coordinate) is negative.
In the first quadrant, the point corresponds to an angle of or . Since we are in the fourth quadrant, the angle is (or radians).
Thus, the angle at the position is 330° (or ).
Would you like more details or have any questions?
Here are 5 related questions:
- How do you determine angles in other quadrants using the unit circle?
- What is the relationship between radians and degrees?
- How do you convert an angle from degrees to radians?
- What are the sine and cosine values for common angles like , , and ?
- How do you find the reference angle for a given angle on the unit circle?
Tip: Knowing key points on the unit circle makes it easier to find angles based on coordinates.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Unit Circle
Radians and Degrees
Formulas
\(\cos(\theta) = \frac{\sqrt{3}}{2}\)
\(\sin(\theta) = -\frac{1}{2}\)
Conversion between radians and degrees
Theorems
Unit Circle Theorem
Suitable Grade Level
Grades 9-12