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keelyjm

  • one year ago

Help finding exact values.

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  1. keelyjm
    • one year ago
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    Find an exact value. sin 75°

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

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

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

  5. keelyjm
    • one year ago
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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.

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

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

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

  9. ZeHanz
    • one year ago
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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?

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

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

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

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

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

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

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

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

  19. phi
    • one year ago
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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

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

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

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

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

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

  25. keelyjm
    • one year ago
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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.

  26. phi
    • one year ago
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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 \[ \frac{ \sqrt{2}-\sqrt{6} }{ 4 }\]

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

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

  29. phi
    • one year ago
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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.

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

  31. ZeHanz
    • one year ago
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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 ;)

  32. keelyjm
    • one year ago
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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

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

  34. ZeHanz
    • one year ago
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    Good for you!

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