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mathslover

  • 2 years ago

sin ( 90 + theta ) = cos theta prove^

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  1. satellite73
    • 2 years ago
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    i guess it depends on what you can use if you can use the addition angle formula, that would work if not maybe with a triangle you can see it

  2. mathslover
    • 2 years ago
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    i want to do with the triangle one but m wondering how will you show (90+theta) in a right angled triangle?

  3. satellite73
    • 2 years ago
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    |dw:1350098235823:dw|

  4. mathslover
    • 2 years ago
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    yes but that is 90 - theta? do 90-theta has any relation with 90 + theta ?

  5. satellite73
    • 2 years ago
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    \[\cos(x)=\frac{a}{c}=\sin(90-x)=-\sin(x-90)\] \[=\sin(x-90+180)=\sin(x+90)\]

  6. mathslover
    • 2 years ago
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    how : -sin(x-90) = sin(x-90+180) ?

  7. satellite73
    • 2 years ago
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    third equal sign because sine is odd, fourth because \(\sin(x)=-\sin(x+180)\)

  8. mathslover
    • 2 years ago
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    Gotcha now, thanks a lot!

  9. satellite73
    • 2 years ago
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    your on the other side of the unit circle |dw:1350098472701:dw|

  10. satellite73
    • 2 years ago
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    yw

  11. mathslover
    • 2 years ago
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    hey, how you did this step? : \[\large{-\sin(x-90) = sin(x-90+180) }\] ?

  12. mathslover
    • 2 years ago
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    @satellite73 did you subtract sin(180) both sides?

  13. satellite73
    • 2 years ago
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    i added 180 inside because \(\sin(x)=-\sin(x+180)\)

  14. mathslover
    • 2 years ago
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    oh k , got it!

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