## Ishaan94 3 years ago Period of $$\Large\frac{|\cos x|}{\sin x}+\frac{|\sin x|}{\cos x}$$?

1. sauravshakya

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2. sauravshakya

IS IT pi?

3. hartnn

2pi, but how

4. sauravshakya

So, the modulas sign makes great difference.

5. hartnn

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

6. sauravshakya

well for that pi

7. sauravshakya

|dw:1348660397213:dw|

8. hartnn

@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

9. hartnn

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

10. sauravshakya

OK

11. sauravshakya

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

12. sauravshakya

|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

13. sauravshakya

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

14. sauravshakya

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.

15. sauravshakya

CORRECT ?

16. phi

yes, the period is 2pi