Question says if...

then find the exact value of sin 3

How would one go about doing this?

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- Nov 13th 2008, 05:27 PMusername11111Finding the exact value of sin 3
Question says if...

then find the exact value of sin 3

How would one go about doing this? - Nov 13th 2008, 05:45 PMmr fantastic
- Nov 13th 2008, 05:48 PMusername11111
- Nov 13th 2008, 05:51 PMmr fantastic
- Nov 13th 2008, 05:53 PMusername11111
- Apr 11th 2012, 01:09 AMDanvanVuuRe: Finding the exact value of sin 3
- Apr 11th 2012, 01:29 AMDanvanVuuRe: Finding the exact value of sin 3
sin 3 = sin 18 - 15 = sin 18 cos 15 - cos 18 sin 15

- Apr 11th 2012, 01:53 AMProve ItRe: Finding the exact value of sin 3
Start with , so . We then have

.

Now note that

To evaluate and , apply the half angle formula to and . Good luck :) - Apr 11th 2012, 01:57 AMbiffboyRe: Finding the exact value of sin 3
cos15=cos(60-45)=cos60cos45+sin60sin45=(1/2)(1/root2)+(root3/2)(1/root2)=(1+root3)/(2root2) whiich simplifies to (root2+root6)/4

Can do similar for sin15 - Apr 11th 2012, 03:03 AMDanvanVuuRe: Finding the exact value of sin 3
sin 18 = (51/2-1)/4

sin 15 = sin 45-30 = sin 45 cos 30 - cos 45 sin 30

cos 18..

cos 15 - Apr 11th 2012, 03:09 AMDanvanVuuRe: Finding the exact value of sin 3
The final awnser looks like this:

sin 3 degrees =

( sqrt( 3 - sqrt(5) + ( 3sqrt(3) - sqrt(15) )/2 ) - sqrt( 5 + sqrt(5) - ( 5sqrt(3) + sqrt(15) )/2 ) )/4 - Apr 12th 2012, 09:13 AMDanvanVuuRe: Finding the exact value of sin 3
Here it is from latex.codecogs:

[IMG]http://latex.codecogs.com/png.latex?\displaystyle%20\begin{align*}\frac{\sqr t{3%20-%20\sqrt{%205%20}%20+%20\frac{\left%28%203%20sqrt{ 3}%20-%20sqrt{15}%20\right%29}{2}}%20-%20\sqrt{5%20+%20\sqrt{%205%20}%20-%20\frac{\left%28%205%20sqrt{3}%20+%20sqrt{15}%20\ right%29}{2}}}{4}\\%20\end{align*}[/IMG] - Apr 14th 2012, 03:25 AMAlibikiRe: Finding the exact value of sin 3
Write 72=45+(30-3) and apply the formulas for the cosine and the sine of a sum of two angles. This will give you an equation involving sin(3) and cos(3), to which you apply the Pythagorean theorem to express cos(3) in terms of sin(3); this will result in a second-order equation in sin(3), whose positive solution you seek.