Help finding exact values.

- anonymous

Help finding exact values.

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- anonymous

Find an exact value.
sin 75°

- anonymous

\[\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\]
Is this right?

- ZeHanz

How did you do it?

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## More answers

- ZeHanz

It is right, but what kind of help are you looking for?

- 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

Do you know the formula: sin(a+b)=sin(a)cos(b)+cos(a)sin(b)?

- 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

I am not familiar with that equation.

- 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

yes to find the final answer.

- ZeHanz

OK, I'll try to draw one...

- anonymous

I have a pic in front of me that I drew

- anonymous

##### 1 Attachment

- 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)

- anonymous

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

- phi

I (for one) switch to degrees first.

- anonymous

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|

- anonymous

So I would do sin(45-30)

- anonymous

phi, when you're done here, can you come back to my problem? thanks!

- anonymous

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

- 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

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...

- anonymous

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.

- anonymous

Alright I will have to write that down. Thank you.

- 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

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

and basically I figured out how to use the equation

- ZeHanz

Good for you!

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