mathslover
  • mathslover
Basic trigonometry help needed.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathslover
  • mathslover
Prove : \(\sin (90 - \theta) = \cos \theta\)
mathslover
  • mathslover
Actually I am confused that how can I : prove that sin in 2nd quadrant is +ve ? That is my basic confusion ...
hartnn
  • hartnn
can u use sin (A-B) formula?

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mathslover
  • mathslover
No idea. Actually that was just in start and the formula arises later, so I think that there must be an easier method?
hartnn
  • hartnn
draw a right triangle
mathslover
  • mathslover
:( not so good but OK ? :)
mathslover
  • mathslover
|dw:1350046739720:dw| nothing is there without naming , OK now I think.
hartnn
  • hartnn
|dw:1350046691525:dw| now find sin 90-theta and cos theta using basic defination
mathslover
  • mathslover
OK wait please !
mathslover
  • mathslover
In case of sin 90 - theta , will perpendicular be : adjacent (base) and base will be opposite?
hartnn
  • hartnn
know the basic defination of sin and cos ? |dw:1350046897401:dw| apply it here, in terms of a and b,c
mathslover
  • mathslover
OH IT IS soh cah toa and not soa cah toa , sorry :(
mathslover
  • mathslover
sin = opposite / hypotenuse cos = adjacent / hypotenuse
hartnn
  • hartnn
yup
mathslover
  • 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
hartnn
  • hartnn
yep, hence proved.
hartnn
  • hartnn
next identity please.
mathslover
  • mathslover
prove that sin in 2nd quadrant is +ve ? That is my basic confusion ...
hartnn
  • hartnn
here, put theta = -theta
hartnn
  • hartnn
and use cos(-theta) = cos theta
mathslover
  • mathslover
how to prove that cos(-theta)=theta ?
mathslover
  • mathslover
again with the use of right triangle @hartnn ?
hartnn
  • hartnn
how will u find -theta in triangle ?
mathslover
  • mathslover
oh yes .. silly me . So, a cartesian plane ?
mathslover
  • mathslover
no, cartesian plane will not work also.
anonymous
  • anonymous
ccw : +ve angle cw : -ve angle
hartnn
  • hartnn
because lengths will be positive , so ratio will always come out to be positive, hence, maybe cartesian plane won't work
mathslover
  • mathslover
Some how agreed .
mathslover
  • mathslover
searched net now, http://www.mathsisfun.com/algebra/trig-four-quadrants.html is that the correct one ?
hartnn
  • 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
mathslover
  • mathslover
doubts ended :) thanks a lo.
mathslover
  • mathslover
*ton/lot.
hartnn
  • hartnn
mathisfun is always a nice reference....
anonymous
  • anonymous
more we knw more confuse we become
hartnn
  • hartnn
more we practice, more the confusion vanishes....
anonymous
  • anonymous
more we practice, more ways we look at things n hence more confusions which ofcourse gives kick ;p

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