Transcription of CHAPTER 10 Limits of Trigonometric Functions
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CHAPTER 10 Limits of Trigonometric Functions
CHAPTER 10 Limits of Trigonometric FunctionsSome limitsinvolve Trigonometric Functions . This CHAPTER explains howto deal with them. Let s begin with the six Trigonometric of the Six Trigonometric FunctionsWe start with the simple limitlimx!csin(x).Herexis a radian measure becausewe are takingsinof it. And becausethe radian measurexapproacesc,weinterpretcas a radian measure picture on the right illustrates pointxon the unit circle moves to-ward the pointcon the circle. As thishappens,sin(x)approaches the numbersin(c). Thuslimx!csin(x)=sin(c).cxsin(x)sin(c)Fo r example,limx! 4sin(x)=sin 4 =p22. With a slight adaption, the abovepicture also showslimx!ccos(x)=cos(c). And applying limit law 5, we getlimx!ctan(x)=limx!csin(x)cos(x)=limx! csin(x)limx!ccos(x)=sin(c)cos(c)=tan(c), provided thatcos(c)6=0, that is,c6= 2+k , wherekis an integer.
that we get the following formulas. lim x!c sin(x) ... It is easy to imagine limits where factoring and canceling is impossible, or for which the limit laws do not apply. For example, in lim x!0 sin(x) x we can’t factor an xfrom the top to cancel the on the bottom (which approaches 0).
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