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highschoolmom2010

  • 2 years ago

Use what you know about trigonometric ratios to show that this equation is an identity.

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  1. highschoolmom2010
    • 2 years ago
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    Sin (x)=cos (x) * tan (x)

  2. highschoolmom2010
    • 2 years ago
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    doesnt make sense to me

  3. katherine.ok
    • 2 years ago
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    you know that tanx = sinx/ cosx/

  4. ganeshie8
    • 2 years ago
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    substitute the sin cos tan wid their ratios (opp, adj, hyp)

  5. katherine.ok
    • 2 years ago
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    so sub tanx= sinx/ cosx. this yields left side. left side= right side. QED

  6. katherine.ok
    • 2 years ago
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    tanx= sinx/ cos x because tanx by definition is opp/ adj. sinx= opp/ hyp cos= adj/hyp.

  7. highschoolmom2010
    • 2 years ago
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    that confused me waay more ^^

  8. completeidiot
    • 2 years ago
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    just a note you can use frac{a}{b} in equations to make fractions ex. \[\frac{a}{b}\]

  9. ganeshie8
    • 2 years ago
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    work left side separately work right side separately show both are equal

  10. completeidiot
    • 2 years ago
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    \[\tan x = \frac{\sin x}{\cos x}\]

  11. ganeshie8
    • 2 years ago
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    left side :- sin x = opp/hyp ---------------(1)

  12. katherine.ok
    • 2 years ago
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    Okay, i will take it really slowly.

  13. katherine.ok
    • 2 years ago
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    sinx= opp/ hyp= left side.

  14. ganeshie8
    • 2 years ago
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    take the right side, substitute opp/adj/hyp, simplify and see if u can get the same as left side

  15. katherine.ok
    • 2 years ago
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    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.

  16. highschoolmom2010
    • 2 years ago
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    \[\frac{ adj }{ hyp }*\frac{ opp }{ adj}\] im really confused :/

  17. ganeshie8
    • 2 years ago
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    keep going, one more step. confusion wil go away

  18. phi
    • 2 years ago
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    adj/adj = 1

  19. katherine.ok
    • 2 years ago
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    top adj can be cancelled out with bottom adj, and you are left with opp/hyp= sinx

  20. highschoolmom2010
    • 2 years ago
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    ok so i was almost there \[\sin (x)=\frac{ opp }{ hyp }\]

  21. highschoolmom2010
    • 2 years ago
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    like that

  22. highschoolmom2010
    • 2 years ago
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    brb yall meh baby is hungry

  23. phi
    • 2 years ago
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    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 \[ \sin(x)=\sin(x) \]

  24. ganeshie8
    • 2 years ago
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    Right hand side :- \(\large \frac{ adj }{ hyp }*\frac{ opp }{ adj} \) \(\large \frac{ \cancel{adj} }{ hyp }*\frac{ opp }{ \cancel{adj}} \) \(\large \frac{ opp }{ hyp } \) ------------(2)

  25. ganeshie8
    • 2 years ago
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    from (1) and (2), left hand side = right hand side. so its an identity.

  26. highschoolmom2010
    • 2 years ago
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    oh ok so how do i write it into words

  27. ganeshie8
    • 2 years ago
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    you wanto write math into words ? hmm

  28. ganeshie8
    • 2 years ago
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    just showing the proof wont do ha ?

  29. highschoolmom2010
    • 2 years ago
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    no i have to write it into words :(

  30. ganeshie8
    • 2 years ago
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    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....

  31. highschoolmom2010
    • 2 years ago
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    ty

  32. ganeshie8
    • 2 years ago
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    np, im sure you can conclude :)

  33. highschoolmom2010
    • 2 years ago
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    yea i think i can :D

  34. highschoolmom2010
    • 2 years ago
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    @phi @katherine.ok @ganeshie8 thank you all for for help

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