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Comparing Trig and Hyperbolic Trig Functions By the Maths Learning Centre, University of Adelaide Trigonometric Functions Hyperbolic Trigonometric Functions Definition using unit circle: If a point is an arc length of t anticlockwise around the unit circle from (1,0), then that point is . (Note the line segment from the origin to the unit circle sweeps out an area of .) Definition using unit hyperbola: If a line segment from the origin to the unit hyperbola sweeps out an area of between (1,0) and a particular point as it moves upwards, then that point is . Parameterising a curve: If we use all values of , the points form the circle with equation Parameterising a curve: If we use all values of , the points form the right-hand branch of the hyperbola with equation . . Defining other functions: Defining other functions: Basic identities Basic identities Double angle identities Double area identities 1 Comparing Trig and Hyperbolic Trig Functions By the Maths Learning Centre, University of Adelaide Trigonometric Functions Odd and even properties Hyperbolic Trigonometric Functions Odd and even properties is an even function is an even function is an even function is an even function is an even function is an even function Values at zero Values at zero Derivatives Derivatives Derivatives of inverse functions Derivatives of inverse functions √ √ √ √ Maclaurin Series Maclaurin Series Relationship to Relationship to 2
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