Transcription of Cosecant, Secant, and Cotangent
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Cosecant, Secant, and Cotangent
Cosecant, Secant, and CotangentIn this chapter we ll introduced three more trigonometric functions: thecosecant, thesecant, and thecotangent. These functions are written as csc( ),sec( ), and cot( ) respectively. They are the functions defined by the formulasbelow:csc( ) =1sin( )sec( ) =1cos( )cot( ) =cos( )sin( )Graphs of cosecant, secant, and cotangent27400 PeriodsCosecant, secant, and Cotangent are periodic functions. Cosecant and se-cant have the same period as sine and cosine do, namely 2 . Cotangenthas period , just as tangent does. In terms of formulas, the previous twosentences mean thatcsc( + 2 ) = csc( )sec( + 2 ) = sec( )cot( + ) = cot( )It s easy to check why these functions have the periods that they do. Forexample, because sine has period 2 that is, because sin( + 2 ) = sin( ) we can check thatcsc( + 2 ) =1sin( + 2 )=1sin( )= csc( )Similarly, the secant function has the same period, 2 , as the function usedto define it, and oddRecall that an even function is a functionf(x) with the property thatf( x) =f(x).
Cosecant, Secant, and Cotangent In this chapter we’ll introduced three more trigonometric functions: the cosecant, the secant, and the cotangent.
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