## mathslover 3 years ago Basic trigonometry help needed.

1. mathslover

Prove : $$\sin (90 - \theta) = \cos \theta$$

2. mathslover

Actually I am confused that how can I : prove that sin in 2nd quadrant is +ve ? That is my basic confusion ...

3. hartnn

can u use sin (A-B) formula?

4. mathslover

No idea. Actually that was just in start and the formula arises later, so I think that there must be an easier method?

5. hartnn

draw a right triangle

6. mathslover

:( not so good but OK ? :)

7. mathslover

|dw:1350046739720:dw| nothing is there without naming , OK now I think.

8. hartnn

|dw:1350046691525:dw| now find sin 90-theta and cos theta using basic defination

9. mathslover

10. mathslover

In case of sin 90 - theta , will perpendicular be : adjacent (base) and base will be opposite?

11. hartnn

know the basic defination of sin and cos ? |dw:1350046897401:dw| apply it here, in terms of a and b,c

12. mathslover

OH IT IS soh cah toa and not soa cah toa , sorry :(

13. mathslover

sin = opposite / hypotenuse cos = adjacent / hypotenuse

14. hartnn

yup

15. mathslover

sin (90-theta) = b/c cos (theta) = b/c and hence sin(90-theta) = cos(theta) , got it now? lol jk. Well is this right @hartnn

16. hartnn

yep, hence proved.

17. hartnn

18. mathslover

prove that sin in 2nd quadrant is +ve ? That is my basic confusion ...

19. hartnn

here, put theta = -theta

20. hartnn

and use cos(-theta) = cos theta

21. mathslover

how to prove that cos(-theta)=theta ?

22. mathslover

again with the use of right triangle @hartnn ?

23. hartnn

how will u find -theta in triangle ?

24. mathslover

oh yes .. silly me . So, a cartesian plane ?

25. mathslover

no, cartesian plane will not work also.

26. sara12345

ccw : +ve angle cw : -ve angle

27. hartnn

because lengths will be positive , so ratio will always come out to be positive, hence, maybe cartesian plane won't work

28. mathslover

Some how agreed .

29. mathslover

searched net now, http://www.mathsisfun.com/algebra/trig-four-quadrants.html is that the correct one ?

30. hartnn

yes, its correct....we could prove it using co-ordinates.... (cos t,sin t)= (x,y) so sin t is +ve in 2nd quadrant

31. mathslover

doubts ended :) thanks a lo.

32. mathslover

*ton/lot.

33. hartnn

mathisfun is always a nice reference....

34. sara12345

more we knw more confuse we become

35. hartnn

more we practice, more the confusion vanishes....

36. sara12345

more we practice, more ways we look at things n hence more confusions which ofcourse gives kick ;p