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lilsis76

  • 3 years ago

using addition formulas for sine and cosine to simplify the expression: cos (2pi/9) cos (pi/18) + sin (2pi/9) sin(pi/18) I want to learn it the normal way first before I add my instructors instructions to place S=45 & T = 30. here are the formulas given: sin(s+t) = sin s cos t + cos s sine t sin(s-t) = sin s cos t - cos s sine t cos(s+t) = cos s cos t - sin s sin t cos(s-t) = cos s cos t + sin s sin t The they way it looks, it seems to use formula 4: cos(s-t) = cos s cos t + sin s sin t

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  1. dpaInc
    • 3 years ago
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    yes.... it is that 4th formula..

  2. lilsis76
    • 3 years ago
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    YAY! okay um... i know that know would i fill it in like this... well wait, first I have a question, how can i find out if its cos or sin that im looking for?

  3. lilsis76
    • 3 years ago
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    wait it would be the cos. right? ugh these formulas are confusing me

  4. dpaInc
    • 3 years ago
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    yes... the cosine one... just remember, the cosine formula (whether it's + or -), is cos * cos +/- sin * sin

  5. lilsis76
    • 3 years ago
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    okay, ill have to put that on a 3by5 card

  6. lilsis76
    • 3 years ago
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    okay! i think i got this just a second. let me know if its right or i made a mistake please.

  7. dpaInc
    • 3 years ago
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    so: \(\large cos(\frac{2\pi}{9}-\frac{\pi}{18})=cos(\frac{2\pi}{9})cos(\frac{\pi}{18})+sin(\frac{2\pi}{9})sin(\frac{\pi}{18}) \)

  8. lilsis76
    • 3 years ago
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    Cos(2pi/9 – pi/18) mult. 2 to the left side……. So cos(4pi/18-pi/18) I guess giving me…….cos 3pi/18? Or do I simplify to get the cos pi/6 ???

  9. dpaInc
    • 3 years ago
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    now... \(\large \frac{2\pi}{9}-\frac{\pi}{18}=\frac{4\pi}{18}-\frac{\pi}{18}=\frac{3\pi}{18}=\frac{\pi}{6} \) that expression actually is cos(pi/6)

  10. dpaInc
    • 3 years ago
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    are you familiar with the unit circle?

  11. lilsis76
    • 3 years ago
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    yes, i had to memorize that thingy

  12. dpaInc
    • 3 years ago
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    wow... you seem like you don't need any help.... :)

  13. lilsis76
    • 3 years ago
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    so...my answer is going to be that unit?

  14. lilsis76
    • 3 years ago
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    ugh?! i do need h

  15. dpaInc
    • 3 years ago
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    so what's cos(pi/6) = ???

  16. lilsis76
    • 3 years ago
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    haha sorry about that. i just need help of steps walking through it, she went so fast in class. i only got pieces

  17. lilsis76
    • 3 years ago
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    30deg

  18. dpaInc
    • 3 years ago
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    yes... cos(pi/6) = cos(30 degrees) = ????

  19. lilsis76
    • 3 years ago
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    the points? is that what the ??? is for?

  20. dpaInc
    • 3 years ago
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    yes.... what's the x-coordinate ??? here is the unit circle...page 3 http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

  21. lilsis76
    • 3 years ago
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    \[\sqrt{3}/2 , 1/2\]

  22. dpaInc
    • 3 years ago
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    i have to leave... sorry... the answer is cos(30 degrees) = \(\large \frac{\sqrt3}{2} \)

  23. lilsis76
    • 3 years ago
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    okay, thank u, bye!

  24. dpaInc
    • 3 years ago
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    the x-coordinate refers to the cosine, the y-coordinate is sine. yw... :)

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