Trigonometry with The Unit Circle

Radians and Degrees

Radian: One radian is the measure of a central angle
that intercepts an arc s equal in length to the
radius r of the circle.
Picture citation:
https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/radian-measure/radian-measure-image002.gif

Radian: One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.

Types of Angles

Coterminal Angles: Angles with the same initial and terminal sides

45 degrees is the coterminal angle of 405 degrees Picture citation: http://www.scienceforums.net/uploads/SAngle.JPG

45 degrees is the coterminal angle of 405 degrees
Picture citation:
http://www.scienceforums.net/uploads/SAngle.JPG

Reference Angle: acute angles formed by the terminal side and the x-axis

Quadrantal Angle: an angle with its terminal side on the x-axis or y-axis

Exact Value vs Approximate Value

Exact Value
Simplified fractions that can include radicals

Approximate Value
A rounded decimal that is found on a calculator

Example
Exact value: √5
__
5
Approximate value: .4472

6 trigonometric functions

Most commonly used:
-sine θ=Opposite/Hypotenuse
-cosecant θ=Adjacent/Hypotenuse
-tangent θ=Opposite/Adajacent

Rarely used:
-cosecant θ=Hypotenuse/Opposite (reciprocal of sine)
-secant θ=Hypotenuse/Adjacent (reciprocal of cosine)
-cotangent θ=Adjacent/Opposite (reciprocal of tangent)

Area of the Sector of a Circle

A=1/2 r2 θ

Angle Vocabulary
Initial side: coincides with the positive x-axis
Terminal side: the side that the angle terminates, or ends, at
Vertex: the point at which the initial side and the terminal side meet
Standard position: when the vertex is at the origin, the initial side coincides with the positive x-axis, and the angle terminates at the terminal side
Picture citation:
http://www.necessaryconclusions.com/wp-content/uploads/2008/04/standard_pos_angle.png