## shruti Group Title how to find the average of sin square theta? one year ago one year ago

1. vikrantg4 Group Title

Don't get it :S

2. Vaidehi09 Group Title

me neither...how can u find the average of just one quantity?

3. apoorvk Group Title

You need $$<\sin^2\theta>$$ right?

4. shruti Group Title

not a quantity.

5. Vaidehi09 Group Title

*just one term

6. shruti Group Title

yes @apoorvk

7. vikrantg4 Group Title

average must be 1/2 ? :P

8. shruti Group Title

how you can say that?

9. apoorvk Group Title

@Vaidehi09 basically that means average value of $$\sin^2\theta$$ in its period - which is $$\pi$$. (the graph for rekindling old memories:)|dw:1343221614291:dw|

10. shruti Group Title

is this graph applicable for that one? @apoorvk

11. vikrantg4 Group Title

You can try integration

12. shruti Group Title

please contineu how to do so.. ? need to integrate it from zero o pi. but in which period or how?

13. vikrantg4 Group Title

$1\div(b-a)\int\limits_{a}^{b}\sin^2\theta d \theta$

14. apoorvk Group Title

For this we need to integrate $$\sin^2\theta$$ from 0 to $$\pi$$,

15. vikrantg4 Group Title

take a = 0 and b = 2pi

16. vikrantg4 Group Title

no bro @apoorvk it should be 2pi

17. Vaidehi09 Group Title

@apoorvk i cant understand why the period is pi.

18. apoorvk Group Title

$\int\limits_0^{\pi}\sin^2\theta.d\theta$ and then I divide this by the difference of the limit, that is $$\pi -0=\pi$$. Basically like the sum of the values by the 'domain covered'.

19. apoorvk Group Title

@Vaidehi09, do you understand that the period sinx of 2pi?

20. Vaidehi09 Group Title

yes

21. shruti Group Title

okay. thanks to all.

22. apoorvk Group Title

now, @Vaidehi09 when I square the function - two changes happen to curve - 1. The curve's shape changes. 2. The negative part of the graph is flipped up in the positive axis. So, whereas the period was 2 pi for sinx, the $$\sin^2x$$ graph repeats itself after every $$\pi$$-distance. Hence the period is pi.

23. vikrantg4 Group Title

OmG ! Expert ! xD Keep it up brother.

24. apoorvk Group Title

Not really :P

25. Vaidehi09 Group Title

@apoorvk ah yes..of course! i was getting confused with the -ve part and what kind of change will happen to the shape of the graph....but i get it now. thanks a lot! :))

26. apoorvk Group Title

No worries :]

27. vikrantg4 Group Title

I am new to calc.. so I am not sure about my replies :P

28. sami-21 Group Title

@apoorvk good Explaination.