trigonometric limits math 120 calculus i djoyce fall 2013 trigonometry is used throughout mathematics especially here in calculus the key to trig in calc is nding the derivatives of the ...
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...Trigonometric limits math calculus i djoyce fall trigonometry is used throughout mathematics especially here in the key to trig calc nding derivatives of sine and cosine functions almost everything else follows from those are dened terms so that means we need know something about derivative function let s see what a f by x lim h when sinx gives sin can t take this limit yet because denominator rewrite numerator using sum formula for sines cos nd sinxcosh cosxsinh cosh sinxlim cosxlim sinh note couple properties expression particular constant times re left with two evaluate will ll rst equals while second it then follow cosx other words these same along cosines you show use geometric analysis involving areas triangles sectors circles nish o sandwich theorem first only positive actually looking at right but since enough shown an acute angle origin smaller triangle sector unit circle contains larger width small its height area sinhcosh whose arc radians has large tanh therefore double div...