Download Trigonometry Review Trig Terms: Angle – An angle is the figure

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Trigonometry Review
Trigonometry began as the computational
component of geometry. If there is anything
that distinguishes trigonometry from the rest
of geometry, it is that trig depends on angle
measurement and quantities determined by
the measure of an angle.
Trig Terms:
Angle – An angle is the figure formed by two rays sharing a common endpoint, called
the vertex of the angle.
Initial Side/Terminal Side – The ray where the measurement of an angle starts is
called the initial side of the angle. The ray where measurement ends is the terminal side.
Vertex – The point at which the sides of an angle meet is called the vertex of the angle.
Standard Position – An angle is considered to be in “standard position,” when the
initial side of the angle is on the x-axis of the Cartesian coordinate system.
Positive angles - Positive angles are measured counter-clockwise from the initial side.
Negative angles – Negative angles are measured clockwise from the initial side.
The measure of an angle is determined by the amount of rotation from it’s initial side to it’s terminal side.
Angles can be measured using several different units. The most commonly seen units are degrees and radians.
One complete revolution of a circle has 360° or 2π radians.
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What the heck is an identity? Well, it’s an equation, but a special kind of equation –
whereas most equations have only one, two, or a finite number of solutions, an identity is
true no matter what value you plug into it (as long as the value is legal – if it makes one
of the functions undefined, all bets are off).
Definition - A trigonometric identity is an equation that is true no matter what angle is
substituted into it.
-Source: Complete Idiot’s Guide to Precalculus by W. Michael Kelley
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What is a Radian?
“Consider a circle of radius 1 and with center at a point C. Let CA and CB be two
radii for which the arc AB of the circle has length 1. Then one radian is taken to be
the measure of the central angle ACB.”
- Source: Schaum’s Outlines: Calculus.
Why Radians?
The motivation for using radian measure in mathematics is this: The value of a trig
function can be thought of as being a fractional part of a circle’s radius. By having a
trig functions’ arguments in units of the circle’s radius, a function’s arguments and
the function’s values are in the same unit.
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