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Mimi_x3

  • one year ago

Write the trigonometric expression as an algebraic expression in u and v. Assume that the variables u and v represent positive real numbers. \[\cos(\sin^{−1}(u)-\tan^{−1}(v))\]

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  1. dan815
    • one year ago
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    okay so what exactly are we doing here

  2. Mimi_x3
    • one year ago
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    Im unsure myself =_=

  3. dan815
    • one year ago
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    you can always eliminate sin and cos with complex versions or power series

  4. dan815
    • one year ago
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    |dw:1443141313790:dw|

  5. dan815
    • one year ago
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    you can try to figure out the inverse function here, for this complex version of sin and cos

  6. dan815
    • one year ago
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    you can also continue to write it in a power series if they prefer that

  7. dan815
    • one year ago
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    my last guess would be to start drawing triangles

  8. dan815
    • one year ago
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    since they have sin^-1(u) so

  9. dan815
    • one year ago
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    u can do the same to the other one

  10. dan815
    • one year ago
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    oh wait oops thats not right

  11. dan815
    • one year ago
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    |dw:1443141590469:dw|

  12. dan815
    • one year ago
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    so ya i think we just gotta do make use of the cos(a-b) indentity

  13. dan815
    • one year ago
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    pretty simple from here, work it out

  14. dan815
    • one year ago
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    |dw:1443142431740:dw|

  15. dan815
    • one year ago
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    =cos(sin^-1(u))*cos(tan^-1(v)) + sin(sin^-1(u)) sin(tan^-1(v)) =sqrt(1-u^2)*1/sqrt(1+u^2) + u* v/sqrt(1+v^2)

  16. dan815
    • one year ago
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    cos(α – β) = cos(α)cos(β) + sin(α)sin(β)

  17. Mimi_x3
    • one year ago
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    Thanks @dan815 My page kept reloading

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