The backbone theorem : the Pythagorean theorem -- Some surprisingly helpful background history -- The basics of "circle-ometry" -- Radian measure -- The graphs of sine and cosine in degrees -- The graphs of sine and cosine in radians -- Basic trigonometric identities -- Sine and cosine for circles of different radii -- A paradigm shift -- The basics of trigonometry -- The tangent, cotangent, secant, and cosecant graphs -- Inverse trigonometric functions -- Addition and subtraction formulas, double and half angle formulas -- The law of cosines -- The area of a triangle -- The law of sines -- Heron's formula for the area of a triangle -- Fitting trigonometric functions to periodic data -- (Extra) Polar coordinates -- (Extra) Polar graphs -- Solutions
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This series of texts proves this so! By collating all the MAA AMC quesitons that link to one particular topic, a coherent mathematical landscape ripe for a guided journey of study emerges. Whether you are motivated by the competition experience or shy away from it, this guide is for you! -- from back cover