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znimon

  • 2 years ago

Evaluate the expression without using a calculator.

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  1. znimon
    • 2 years ago
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    \[\sin (\pi/3) + \cos (\pi/3)\]

  2. znimon
    • 2 years ago
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    An entry level explanation would be useful.

  3. myko
    • 2 years ago
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    Pi/3=60º as is well known cos60º=1/2 and sin60º=sqrt3/2

  4. satellite73
    • 2 years ago
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  5. znimon
    • 2 years ago
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    Should I have converted them to degrees then?

  6. satellite73
    • 2 years ago
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    allow me to disagree with @myko this question has nothing to do with degrees. forget degrees it has to do with numbers find the sine and cosine from the coordinates on the unit circle

  7. myko
    • 2 years ago
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    if it is more clear for you, then yes, if not just stay with radians

  8. satellite73
    • 2 years ago
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    do not start a trig problem by converting numbers to degrees, it is a bad habit and will mess you up later if you are working with numbers, stick with numbers

  9. myko
    • 2 years ago
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    degrees are just, sometimes, more evident to place a apoint in the circle. But I agree with @satellite73 that it is more strait with rad

  10. satellite73
    • 2 years ago
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    sine and cosine are functions of numbers, not angles. they correspond to the functions of angles if the angles are measured in radians

  11. znimon
    • 2 years ago
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    alright that seems to make sense. Will you walk me through what you mean by "find the sine and cosine from the coordinates on the unit circle?"

  12. satellite73
    • 2 years ago
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    look at the last page of the cheat sheet i sent locate the point on the unit circle corresponding to \(\frac{\pi}{3}\) 2x ^{5}+x ^{3}-7x+14

  13. satellite73
    • 2 years ago
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    corresponding to \(\frac{\pi}{3}\)

  14. znimon
    • 2 years ago
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    alright I see an ordered pair that looks suspiciously like sin and cos that you mentioned earlier

  15. satellite73
    • 2 years ago
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    you should see the ordered pair \((\frac{1}{2},\frac{\sqrt{3}}{2})\) the first coordinate is \(\cos(\frac{\pi}{3})\) and the second coordinate is \(\sin(\frac{\pi}{3})\)

  16. znimon
    • 2 years ago
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    So what if this is on a test and I'm not allowed the cheat sheet?

  17. znimon
    • 2 years ago
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    This one seems fairly easy now I know this forms a 60 30 90 triangle but what about something more irregular or do these always form 30-60-90 or 45-45-90 triangles?

  18. znimon
    • 2 years ago
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    @satellite73

  19. znimon
    • 2 years ago
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    (The ones they ask me to solve without a calculator.)

  20. znimon
    • 2 years ago
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    @satellite73

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