anonymous
  • anonymous
Help finding exact values.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Find an exact value. sin 75°
anonymous
  • anonymous
\[\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\] Is this right?
ZeHanz
  • ZeHanz
How did you do it?

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ZeHanz
  • ZeHanz
It is right, but what kind of help are you looking for?
anonymous
  • anonymous
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.
ZeHanz
  • ZeHanz
Do you know the formula: sin(a+b)=sin(a)cos(b)+cos(a)sin(b)?
anonymous
  • anonymous
Like currently I am stuck on Find an exact value. sine of negative eleven pi divided by twelve.\[\sin(-\frac{ 11\pi }{ 12 })\]
anonymous
  • anonymous
I am not familiar with that equation.
ZeHanz
  • ZeHanz
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?
anonymous
  • anonymous
yes to find the final answer.
ZeHanz
  • ZeHanz
OK, I'll try to draw one...
anonymous
  • anonymous
I have a pic in front of me that I drew
anonymous
  • anonymous
phi
  • phi
I think you try to use "nice numbers" that add or subtract to get 75º 45º + 30º = 75º
phi
  • phi
now use sin(a+b)= sin(a)cos(b) + cos(a) sin(b)
anonymous
  • anonymous
I already figured that one out. I am working on\[\sin(-\frac{ 11\pi }{ 12 })\]
phi
  • phi
I (for one) switch to degrees first.
anonymous
  • anonymous
how do I do that?
phi
  • phi
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
phi
  • phi
|dw:1360100026509:dw|
anonymous
  • anonymous
So I would do sin(45-30)
anonymous
  • anonymous
phi, when you're done here, can you come back to my problem? thanks!
anonymous
  • anonymous
so would I do sin(45)cos(30)-cos(45)sin(30) next?
phi
  • phi
yes, but remember that sin is negative in the 3rd quadrant so minus the final answer
anonymous
  • anonymous
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.
phi
  • phi
sin(45)cos(30)-cos(45)sin(30) should give you \[ \frac{ \sqrt{6}-\sqrt{2} }{ 4 }\] now negate it to get \[ \frac{ \sqrt{2}-\sqrt{6} }{ 4 }\]
phi
  • phi
you can always check your answers using a calculator. sin(-165º) = -0.2588...
anonymous
  • anonymous
Oh I wrote it wrong and forgot to negate it
phi
  • phi
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.
anonymous
  • anonymous
Alright I will have to write that down. Thank you.
ZeHanz
  • ZeHanz
@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 ;)
anonymous
  • anonymous
Yeah after I saw that with unusual angles you had to split it into to normal angles I got where a and b went
anonymous
  • anonymous
and basically I figured out how to use the equation
ZeHanz
  • ZeHanz
Good for you!

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