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Radian Measure and the Circular Functions

This page is meant to serve as a quick overview of radian measurement and the circular functions.

Radian Measure

Radian measure of any angle is the length of the arc intercepted on a circle with a radius of 1 by an angle in the standard position on a coordinate plane.

Degree / Radian Relationship

180° = π radians

Degree / Radian Conversions

1. To convert a radian measure to degrees, multiply a radian measure by 180°/π and simplify.
2. To convert a degrees measure to radians, multiply a radian measure by π/180° and simplify.

Arc Length

The arc length, s, is the measure of the distance along the curved line making up the arc. The length of the arc, s, intercepted on a circle by a central angle of Θ, can be determined by s=

Area of Sector

The arc length, s, is the measure of the distance along the curved line making up the arc. The length of the arc, s, intercepted on a circle by a central angle of Θ, can be determined by A=(1/2)(r²Θ)

The Unit Circle

Cicular Functions

For the six circular functions, start with the point (1,0) and \lay off an arc length of s along the circle. If s is counterclockwise, it is positive, where if its clockwise, it is negative. Let the entpoint of the arc be (x,y).

sin s = y cos s = x tan s = y / x
csc s = 1 / y sec s = 1 / x cot s = x / y

Domains of the Circular Functions

So long that n is any integer, the somains of the circular functions are as follows

Sine and Cosine Functions (-∞,∞)
Tangent and Secant Functions {s|s ≠ π/2 + nπ}
Cotangent and Cosecant Functions {s|s ≠ nπ}

Angular Velocity

ω = Θ / t
(ω in radians per unit of time with Θ in radians)

Linear Velocity

v = s / t
v = / t
v =