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anonymous

  • one year ago

Determine the sign of sin five pi divided by four without using a calculator.

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  1. welshfella
    • one year ago
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    |dw:1435357223930:dw|

  2. anonymous
    • one year ago
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    Can you explain to me how to find that? @welshfella :)

  3. welshfella
    • one year ago
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    what is the sign of opposite / hypotenuse from the diagram

  4. welshfella
    • one year ago
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    positive angles go anticlockwise one half a rev is pi and 5pi/4 is another p/4 the signs of the lines are marked

  5. welshfella
    • one year ago
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    sin 5pi/4 = - / + = -

  6. anonymous
    • one year ago
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    Both hypotenuse and opposite are negative.

  7. welshfella
    • one year ago
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    No hypotenuse is always positive

  8. anonymous
    • one year ago
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    Oops! I was looking at the wrong part. That was the adj.

  9. welshfella
    • one year ago
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    yes the tangent is positive -/- in 3rd quadrant

  10. anonymous
    • one year ago
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    "positive angles go anticlockwise" what do you mean by this?

  11. anonymous
    • one year ago
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    So the answer would be negative, right? But can you explain to me the steps how to find it? I'm so confused right now. Like what do I need to do first?

  12. welshfella
    • one year ago
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    they are measured in an anticlockwise direction angles measured in clockwise direction are negative - that the convention 5pi/4 is equivalent to -3pi/4

  13. anonymous
    • one year ago
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    \[\sin \frac{ 5 \pi }{ 4 }=\sin \left( \pi+\frac{ \pi }{ 4 } \right)=-\sin \frac{ \pi }{ 4 }=-\frac{ 1 }{ \sqrt{2} }\]

  14. welshfella
    • one year ago
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    well i've done it using the unit circle . You can also use identities to do these just as surjithayer has just done.

  15. welshfella
    • one year ago
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    the 1 / sqrt2 comes from the standard triangle |dw:1435358195274:dw|

  16. anonymous
    • one year ago
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    @surjithayer How did you get \[-\sin \pi/4?\]

  17. welshfella
    • one year ago
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    sin pi/4 = 1/sqrt2 therefor - sin pi/4 = -1/sqrt2

  18. anonymous
    • one year ago
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    \[\sin \left( \pi+\beta \right)=-\sin \beta \] sin is negative in 3rd quadrant.

  19. anonymous
    • one year ago
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    Thanks for the help! @surjithayer @welshfella . I'm still kinda confused, but I think I get it now. :)

  20. welshfella
    • one year ago
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    yw

  21. anonymous
    • one year ago
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    \[\sin \left( \pi+x \right)=\sin \pi \cos x+\cos \pi \sin x\] \[\sin \pi=0,\cos \pi=-1\]

  22. welshfella
    • one year ago
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    its just a personal thing but I find it easier to use diagrams for this type of problem

  23. anonymous
    • one year ago
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    @welshfella maybe to visualize the problem? Both ways suit for me though. :)

  24. welshfella
    • one year ago
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    that s good

  25. anonymous
    • one year ago
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    If I change sin five pi divided by four to, let's say, \[\tan \frac{5\pi }{ 4 }\], what will be the answer? I just want to practice haha.

  26. anonymous
    • one year ago
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    Will it be positive?

  27. anonymous
    • one year ago
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    yes it is in 3rd quadrant

  28. anonymous
    • one year ago
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    Okay, so can I also assume that cos 5pi/4 is negative based on the All Students Take Calculus?

  29. anonymous
    • one year ago
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    yes

  30. anonymous
    • one year ago
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    in 3rd quadrant only tan and cot are positive.

  31. anonymous
    • one year ago
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    Yes, since cot is just the reciprocal of tan. :)

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