Define the unit circle in trigonometry
Answer 1
Abigail Nelson
The unit circle is a circle with a radius of 1 unit, centered at the origin $(0, 0)$ in the Cartesian coordinate system. It is primarily used in trigonometry to define sine, cosine, and tangent functions:
1. Any point $(x, y)$ on the unit circle satisfies the equation:
$$ x^2 + y^2 = 1 $$
2. For an angle $\theta$ measured from the positive $x$-axis, the coordinates of the corresponding point on the circle are:
$$ (\cos(\theta), \sin(\theta)) $$
3. The unit circle allows periodicity and symmetry properties of trigonometric functions to be observed geometrically.
Answer 2
Alex Thompson
The unit circle is a circle with radius 1, centered at $(0, 0)$, used to define trigonometric functions where:
$$ x^2 + y^2 = 1 $$
The coordinates of any point are $ (\cos(\theta), \sin(\theta)) $.
Answer 3
Amelia Mitchell
The unit circle is a circle with radius 1 centered at $(0, 0)$, defined by:
$$ x^2 + y^2 = 1 $$
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