Unit Circle

What is the radius of the unit circle?

1 unit

What is the equation of the unit circle?

x^2 + y^2 = 1

How is an angle in standard position defined?

An angle with its vertex at the origin and its initial side along the positive x-axis.

How are angles typically measured in the unit circle?

In radians, though degrees can also be used.

What is the conversion formula from degrees to radians?

radians = degrees × π/180°

What is the sine function in relation to the unit circle?

The y-coordinate of the point on the unit circle; sin(θ) = y.

What is the cosine function in relation to the unit circle?

The x-coordinate of the point on the unit circle; cos(θ) = x.

What is the tangent function defined as in relation to sine and cosine?

tan(θ) = y/x = sin(θ)/cos(θ) (provided x ≠ 0).

What is cosecant in relation to sine?

The reciprocal of sine; csc(θ) = 1/y = 1/sin(θ) (provided y ≠ 0).

What are the coordinates at the angle of π/4 (45°) on the unit circle?

(√2/2, √2/2).

What is the mnemonic for remembering positive trigonometric functions in each quadrant?

All Students Take Calculus.

What are the coordinates at the angle of π (180°) on the unit circle?

(-1, 0).

List the coordinates at π/2 (90°) on the unit circle.

(0, 1).

What do the coordinates (1, 0) represent on the unit circle?

The angle 0 or 2π (0° or 360°).

What is the relationship between radians and degrees for π radians?

π radians = 180°.

What is the tangent function if x = 0?

Undefined.