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22Nov2012.ink 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. 1 22Nov2012.ink 2 22Nov2012.ink 3 22Nov2012.ink 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 4 22Nov2012.ink 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. 5 22Nov2012.ink 6