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anonymous

  • one year ago

The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

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  1. Michele_Laino
    • one year ago
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    |dw:1438268412570:dw|

  2. anonymous
    • one year ago
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    So can you explain that? lol

  3. Michele_Laino
    • one year ago
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    it is the representation of your problem

  4. Michele_Laino
    • one year ago
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    now, we can write this: \[\Large OP = \sqrt {{2^2} + {3^2}} = ...\]

  5. Michele_Laino
    • one year ago
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    what is OP?

  6. Michele_Laino
    • one year ago
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    I have applied the Theorem of Pitagora to the triangle OP1P

  7. anonymous
    • one year ago
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    the sin tan and cos?

  8. Michele_Laino
    • one year ago
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    yes, we have to compute OP first

  9. anonymous
    • one year ago
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    ok

  10. Michele_Laino
    • one year ago
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    hint: \[\Large OP = \sqrt {{2^2} + {3^2}} = \sqrt {4 + 9} = ...?\]

  11. anonymous
    • one year ago
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    is it just square root of 13

  12. Michele_Laino
    • one year ago
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    yes!

  13. anonymous
    • one year ago
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    so thats the answer

  14. anonymous
    • one year ago
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    for all three

  15. Michele_Laino
    • one year ago
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    no, since we have to apply these formulas: \[\Large \begin{gathered} \cos \theta = \frac{{O{P_1}}}{{OP}} = \frac{2}{{\sqrt {13} }} = ... \hfill \\ \hfill \\ \sin \theta = \frac{{P{P_1}}}{{OP}} = \frac{3}{{\sqrt {13} }} = ... \hfill \\ \end{gathered} \]

  16. Michele_Laino
    • one year ago
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    finally, by definition, we can write: \[\Large \tan \theta = \frac{{P{P_1}}}{{O{P_1}}} = ...\]

  17. anonymous
    • one year ago
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    3/2?

  18. Michele_Laino
    • one year ago
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    yes!

  19. anonymous
    • one year ago
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    sweet thanks for the help!

  20. Michele_Laino
    • one year ago
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    :)

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