highschoolmom2010
  • highschoolmom2010
Use what you know about trigonometric ratios to show that this equation is an identity.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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highschoolmom2010
  • highschoolmom2010
Sin (x)=cos (x) * tan (x)
highschoolmom2010
  • highschoolmom2010
doesnt make sense to me
anonymous
  • anonymous
you know that tanx = sinx/ cosx/

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More answers

ganeshie8
  • ganeshie8
substitute the sin cos tan wid their ratios (opp, adj, hyp)
anonymous
  • anonymous
so sub tanx= sinx/ cosx. this yields left side. left side= right side. QED
anonymous
  • anonymous
tanx= sinx/ cos x because tanx by definition is opp/ adj. sinx= opp/ hyp cos= adj/hyp.
highschoolmom2010
  • highschoolmom2010
that confused me waay more ^^
anonymous
  • anonymous
just a note you can use frac{a}{b} in equations to make fractions ex. \[\frac{a}{b}\]
ganeshie8
  • ganeshie8
work left side separately work right side separately show both are equal
anonymous
  • anonymous
\[\tan x = \frac{\sin x}{\cos x}\]
ganeshie8
  • ganeshie8
left side :- sin x = opp/hyp ---------------(1)
anonymous
  • anonymous
Okay, i will take it really slowly.
anonymous
  • anonymous
sinx= opp/ hyp= left side.
ganeshie8
  • ganeshie8
take the right side, substitute opp/adj/hyp, simplify and see if u can get the same as left side
anonymous
  • anonymous
cosx= adj/ hyp; tan x= opp/adj . cosx* tanx= (adj/hyp) (opp/adj); notice adj can be cancelled out--> opp/ hyp= sinx. Notice it is same as sinx= left side.
highschoolmom2010
  • highschoolmom2010
\[\frac{ adj }{ hyp }*\frac{ opp }{ adj}\] im really confused :/
ganeshie8
  • ganeshie8
keep going, one more step. confusion wil go away
phi
  • phi
adj/adj = 1
anonymous
  • anonymous
top adj can be cancelled out with bottom adj, and you are left with opp/hyp= sinx
highschoolmom2010
  • highschoolmom2010
ok so i was almost there \[\sin (x)=\frac{ opp }{ hyp }\]
highschoolmom2010
  • highschoolmom2010
like that
highschoolmom2010
  • highschoolmom2010
brb yall meh baby is hungry
phi
  • phi
the other way is to say \[ \tan(x) = \frac{\sin(x)}{\cos(x)}\] replace tan(x) in \[ \sin(x)= \cos(x) \tan(x) \\ \sin(x)= \cos(x)\frac{\sin(x)}{\cos(x)}\] then notice that cos(x)/cos(x) is 1 you get \[ \sin(x)=\sin(x) \]
ganeshie8
  • ganeshie8
Right hand side :- \(\large \frac{ adj }{ hyp }*\frac{ opp }{ adj} \) \(\large \frac{ \cancel{adj} }{ hyp }*\frac{ opp }{ \cancel{adj}} \) \(\large \frac{ opp }{ hyp } \) ------------(2)
ganeshie8
  • ganeshie8
from (1) and (2), left hand side = right hand side. so its an identity.
highschoolmom2010
  • highschoolmom2010
oh ok so how do i write it into words
ganeshie8
  • ganeshie8
you wanto write math into words ? hmm
ganeshie8
  • ganeshie8
just showing the proof wont do ha ?
highschoolmom2010
  • highschoolmom2010
no i have to write it into words :(
ganeshie8
  • ganeshie8
okay then describe wat we just did, you may start like below :- since left hand side is sinx, and we knw that sinx = opp/hyp, proving right hand side simplifies to opp/hyp is sufficient to prove that given equation is an identity. right hand side we have cosx * tanx. substituting their respective trig ratios, we get adj/hyp * opp/adj....
highschoolmom2010
  • highschoolmom2010
ty
ganeshie8
  • ganeshie8
np, im sure you can conclude :)
highschoolmom2010
  • highschoolmom2010
yea i think i can :D
highschoolmom2010
  • highschoolmom2010
@phi @katherine.ok @ganeshie8 thank you all for for help

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