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

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

Mathematics
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|dw:1348659986687:dw|
IS IT pi?
2pi, but how

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Other answers:

So, the modulas sign makes great difference.
for simplicity, first try |sin x|+|cos x| @sauravshakya
well for that pi
|dw:1348660397213:dw|
@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
1 Attachment
@sauravshakya plot the sum, not individually, i also made that mistake and got pi, but its pi/2
OK
THIS MAY ALSO WORK: IsinxI+IcosxI=IsinxI + Isin(90-x)I
|dw:1348661004454:dw| NOW, x y 0-45 +ve 45-90 +ve 90-135 -ve 135-180 +ve 180-225 -ve 225-270 -ve 270-315 +ve 315-360 -ve
THAT CLEARLY SHOWS PERIOD MUST BE greater than or equal to 360 degree
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.
CORRECT ?
  • phi
yes, the period is 2pi

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