Can someone guide me through finding sin 105 degrees using the half angle formula?

Question

dtan5457 · Answer

This is what I have so far.

210 degrees

$$\pm \sqrt{\frac{ 1-\frac{ \sqrt{3} }{ 2 } }{ 2 }}$$

dtan5457 · Answer

so far so good?

amorfide · Answer

yes because you have subbed into a half angle formula for sinx/2

dtan5457 · Answer

then next step, i should just to cancel some denominators by multipying each term by 2?

amorfide · Answer

I would get rid of the fraction in the top of the fraction first by multiplying top and bottom by 2
then trying to bring stuff out of the root

superdavesuper · Answer

hmmm try 210 = 180 + 30 and then apply sin(A+B) = sinAcosB + cosAsinB...

amorfide · Answer

that is addition formula not half angle formula is it not?

amorfide · Answer

anyway carry on, since you have done it correctly assuming that cos(105)=root3/2

dtan5457 · Answer

so leave the denominator alone for now, and just multiply the top part by 2/2?

amorfide · Answer

$$\frac{ 1-\frac{ \sqrt{3} }{ 2} }{ 2 }= \frac{ 2(1)- \frac{ 2\sqrt{3} }{ 2 } }{2(2)  }$$

amorfide · Answer

then obviously put your square root back

amorfide · Answer

after that step you are pretty much finished to be honest

dtan5457 · Answer

im getting
$$\frac{ \sqrt{2-\sqrt{3}} }{ 2 }$$

dtan5457 · Answer

is my answer correct?

amorfide · Answer

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