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keelyjm

Help finding exact values.

  • one year ago
  • one year ago

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  1. keelyjm
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    Find an exact value. sin 75°

    • one year ago
  2. keelyjm
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    \[\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\] Is this right?

    • one year ago
  3. ZeHanz
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    How did you do it?

    • one year ago
  4. ZeHanz
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    It is right, but what kind of help are you looking for?

    • one year ago
  5. keelyjm
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    I do not know how to do it, but looking at a unit circle that seemed correct with where the angle should be. I want to know what equatin to use to get that answer for future use.

    • one year ago
  6. ZeHanz
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    Do you know the formula: sin(a+b)=sin(a)cos(b)+cos(a)sin(b)?

    • one year ago
  7. keelyjm
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    Like currently I am stuck on Find an exact value. sine of negative eleven pi divided by twelve.\[\sin(-\frac{ 11\pi }{ 12 })\]

    • one year ago
  8. keelyjm
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    I am not familiar with that equation.

    • one year ago
  9. ZeHanz
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    OK, that makes it a lot more difficult, I guess. sin(-11pi/12)=-sin(11pi/12)=-sin(pi/12)=-sin(15°) Have you been instructed to do these kind of problems in a unit circle?

    • one year ago
  10. keelyjm
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    yes to find the final answer.

    • one year ago
  11. ZeHanz
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    OK, I'll try to draw one...

    • one year ago
  12. keelyjm
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    I have a pic in front of me that I drew

    • one year ago
  13. keelyjm
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    • one year ago
  14. phi
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    I think you try to use "nice numbers" that add or subtract to get 75º 45º + 30º = 75º

    • one year ago
  15. phi
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    now use sin(a+b)= sin(a)cos(b) + cos(a) sin(b)

    • one year ago
  16. keelyjm
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    I already figured that one out. I am working on\[\sin(-\frac{ 11\pi }{ 12 })\]

    • one year ago
  17. phi
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    I (for one) switch to degrees first.

    • one year ago
  18. keelyjm
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    how do I do that?

    • one year ago
  19. phi
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    multiply by 180/pi you get -165 degrees that means go clockwise from the x-axis. as a positive angle it is 360-165= 195 degrees so you want to find the sin(15) in the 3rd quadrant

    • one year ago
  20. phi
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    |dw:1360100026509:dw|

    • one year ago
  21. keelyjm
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    So I would do sin(45-30)

    • one year ago
  22. mariomintchev
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    phi, when you're done here, can you come back to my problem? thanks!

    • one year ago
  23. keelyjm
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    so would I do sin(45)cos(30)-cos(45)sin(30) next?

    • one year ago
  24. phi
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    yes, but remember that sin is negative in the 3rd quadrant so minus the final answer

    • one year ago
  25. keelyjm
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    So how would I do that? I am thinking the answer would be \[\frac{ -\sqrt{6}-\sqrt{2} }{ 4 }\] Just from what I know so far and the unit circle.

    • one year ago
  26. phi
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    sin(45)cos(30)-cos(45)sin(30) should give you \[ \frac{ \sqrt{6}-\sqrt{2} }{ 4 }\] now negate it to get \[ \frac{ \sqrt{2}-\sqrt{6} }{ 4 }\]

    • one year ago
  27. phi
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    you can always check your answers using a calculator. sin(-165º) = -0.2588...

    • one year ago
  28. keelyjm
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    Oh I wrote it wrong and forgot to negate it

    • one year ago
  29. phi
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    so to do these problems, figure out the "reference angle" (that is the angle less than 90 that you make with the x-axis) and what quadrant. try to come up with sums or differences that give the reference angle and then use the formulas finally, use the quadrant to assign the correct sign.

    • one year ago
  30. keelyjm
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    Alright I will have to write that down. Thank you.

    • one year ago
  31. ZeHanz
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    @keelyjm: I thought you weren't familiar with sin(a+b)=sin(a)cos(b)+cos(a)sin(b)? Now you are using it... Glad you do, because it makes everything much easier ;)

    • one year ago
  32. keelyjm
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    Yeah after I saw that with unusual angles you had to split it into to normal angles I got where a and b went

    • one year ago
  33. keelyjm
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    and basically I figured out how to use the equation

    • one year ago
  34. ZeHanz
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    Good for you!

    • one year ago
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