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lilsis76

  • 3 years ago

Use the formula cos(s+t)=cos s cos t - sin s sin t: to compute the exact value of cos 75 degrees. all i know is that 75 degrees is between 90 deg and 60 degrees on a unit circle.

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  1. zepdrix
    • 3 years ago
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    Hmmmmm we have special angles for 30, 45, 60, 90... do any of those 2 add up to 75? Cause that would really help us out in this problem.

  2. lilsis76
    • 3 years ago
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    well... okay we have the 30 and 45 angles

  3. zepdrix
    • 3 years ago
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    Hmm good good :) I think we can work with that. So we'll rewrite cos(75) as cos(45+30). After we apply the sum formula, we should be able to plug in a BUNCH of special angles and HOPEFULLY we'll be able to simplify it :3 hehe

  4. zepdrix
    • 3 years ago
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    So use your formula you posted at the top, what will your setup look like? :D

  5. lilsis76
    • 3 years ago
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    okay.

  6. lilsis76
    • 3 years ago
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    the 45 will be the s, and t will be tht 30 so... cos(s+t)=cos s cos t - sin s sin t: cos(45+30)= cos 45 cos 30 - sin 45 sin 30. yes??

  7. zepdrix
    • 3 years ago
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    Mmmmmmmmmmmmmm yah looks good. Now it's special angle time! :OOO

  8. lilsis76
    • 3 years ago
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    what does that mean?

  9. zepdrix
    • 3 years ago
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    Let's look at the first ..thing.. cos(45), what is the cosine of 45 degrees? It's a special angle that you're suppose to remember.. (from the unit circle) :X

  10. lilsis76
    • 3 years ago
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    OH....so the points are the special angles??? I thought that meant another formula to remember. um... 45 is at squ rt. 2 / squ rt. 2 / 2 cos sin cos is squ.rt. 2 / 2

  11. zepdrix
    • 3 years ago
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    so cos(45)=sqrt2/2 and cos(30)? :D Go through all of them and do yer magic!

  12. lilsis76
    • 3 years ago
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    what?! the 30 ? um... hold on

  13. lilsis76
    • 3 years ago
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    squ rt 3 /2

  14. lilsis76
    • 3 years ago
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    okay hold on lol

  15. zepdrix
    • 3 years ago
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    so our first term cos(45)cos(30) becomes.. (sqrt2/2)(sqrt3/2) Which we should be able to simplify a little bit. hmm

  16. lilsis76
    • 3 years ago
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    okay tis.. (sqrt2 /2)( sqrt3/2) - (sqrt 2/2)(1/2)

  17. zepdrix
    • 3 years ago
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    k good good c: Now simplyyyyyyyyyy \:D/

  18. lilsis76
    • 3 years ago
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    uh...hold on let me try doin it um..

  19. lilsis76
    • 3 years ago
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    i get sqrt3 /2 - 1/2

  20. zepdrix
    • 3 years ago
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    |dw:1350602295589:dw| Hmmmm this is what I'm coming up with D:

  21. lilsis76
    • 3 years ago
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    okay, but wouldn't it be - sqrt 4 /2?

  22. zepdrix
    • 3 years ago
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    Water you talking about? D:

  23. lilsis76
    • 3 years ago
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    like okay, wouldnt the sqrt 6 / 4 - sqrt2/4 be a sqrt 4/4 leading to 2/4=1/2 ?

  24. zepdrix
    • 3 years ago
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    No you can't subtract those sqrt's like that :c you have to leave them alone.

  25. lilsis76
    • 3 years ago
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    okay, so next time i get sq roots like that, just leave it alone?

  26. zepdrix
    • 3 years ago
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    Yah that is a good place to stop c: \[\frac{ \sqrt6 -\sqrt2 }{ 4 }\]

  27. lilsis76
    • 3 years ago
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    okay then, thank you for helping me :D

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