Unit Circle

What is the Unit Circle?

A circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

What is the equation represented by the Unit Circle?

x^2 + y^2 = 1

In terms of the unit circle, what trigonometric function corresponds to the x-coordinate?

\cos(\theta)

In terms of the unit circle, what trigonometric function corresponds to the y-coordinate?

\sin(\theta)

How is \tan(\theta) defined using the coordinates of the unit circle?

\tan(\theta) = \frac{y}{x} (where x \neq 0)

What are the coordinates at 0 radians (0^\circ)?

(1, 0)

What are the coordinates at \frac{\pi}{6} (30^\circ)?

(\frac{\sqrt{3}}{2}, \frac{1}{2})

What are the coordinates at \frac{\pi}{4} (45^\circ)?

(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})

What are the coordinates at \frac{\pi}{3} (60^\circ)?

(\frac{1}{2}, \frac{\sqrt{3}}{2})

What are the coordinates at \frac{\pi}{2} (90^\circ)?

(0, 1)

In which quadrants is the sine function (y-value) positive?

Quadrants I and II

In which quadrants is the cosine function (x-value) positive?

Quadrants I and IV