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highschoolmom2010
Use what you know about trigonometric ratios to show that this equation is an identity.
Sin (x)=cos (x) * tan (x)
doesnt make sense to me
you know that tanx = sinx/ cosx/
substitute the sin cos tan wid their ratios (opp, adj, hyp)
so sub tanx= sinx/ cosx. this yields left side. left side= right side. QED
tanx= sinx/ cos x because tanx by definition is opp/ adj. sinx= opp/ hyp cos= adj/hyp.
that confused me waay more ^^
just a note you can use frac{a}{b} in equations to make fractions ex. \[\frac{a}{b}\]
work left side separately work right side separately show both are equal
\[\tan x = \frac{\sin x}{\cos x}\]
left side :- sin x = opp/hyp ---------------(1)
Okay, i will take it really slowly.
sinx= opp/ hyp= left side.
take the right side, substitute opp/adj/hyp, simplify and see if u can get the same as left side
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.
\[\frac{ adj }{ hyp }*\frac{ opp }{ adj}\] im really confused :/
keep going, one more step. confusion wil go away
top adj can be cancelled out with bottom adj, and you are left with opp/hyp= sinx
ok so i was almost there \[\sin (x)=\frac{ opp }{ hyp }\]
brb yall meh baby is hungry
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 \[ \sin(x)=\sin(x) \]
Right hand side :- \(\large \frac{ adj }{ hyp }*\frac{ opp }{ adj} \) \(\large \frac{ \cancel{adj} }{ hyp }*\frac{ opp }{ \cancel{adj}} \) \(\large \frac{ opp }{ hyp } \) ------------(2)
from (1) and (2), left hand side = right hand side. so its an identity.
oh ok so how do i write it into words
you wanto write math into words ? hmm
just showing the proof wont do ha ?
no i have to write it into words :(
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....
np, im sure you can conclude :)
yea i think i can :D
@phi @katherine.ok @ganeshie8 thank you all for for help