Ishaan94
Period of \(\Large\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x}\)?



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sauravshakya
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dw:1348659986687:dw

sauravshakya
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IS IT pi?

hartnn
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2pi, but how

sauravshakya
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So, the modulas sign makes great difference.

hartnn
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for simplicity, first try sin x+cos x @sauravshakya

sauravshakya
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well for that pi

sauravshakya
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dw:1348660397213:dw

hartnn
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@Ishaan94 i plotted sin x+cos x
its period is coming out to be 90, 4 lobes in 360....u are correct, its pi/2, not pi

hartnn
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@sauravshakya plot the sum, not individually, i also made that mistake and got pi, but its pi/2

sauravshakya
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OK

sauravshakya
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THIS MAY ALSO WORK:
IsinxI+IcosxI=IsinxI + Isin(90x)I

sauravshakya
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dw:1348661004454:dw
NOW,
x y
045 +ve
4590 +ve
90135 ve
135180 +ve
180225 ve
225270 ve
270315 +ve
315360 ve

sauravshakya
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THAT CLEARLY SHOWS PERIOD MUST BE greater than or equal to 360 degree

sauravshakya
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BUT IT CANNOT BE greater than 360 degree as same pattern will repeat as the values of sin1 and sin 361 are same........ THUS the period is 360 degree.

sauravshakya
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CORRECT ?

phi
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yes, the period is 2pi