Help finding exact values.

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Help finding exact values.

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Find an exact value. sin 75°
\[\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\] Is this right?
How did you do it?

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Other answers:

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

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