SOLUTION: What is the exact value of sin ((22 1/2)degrees) using sum and difference?
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Question 461701: What is the exact value of sin ((22 1/2)degrees) using sum and difference?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the Half-Angle Formula for Sine which follows directly from the Double Angle Formula for Cosine which follows directly from the Sum Formula for Cosine. See Double Angle and Half Angle Formulas for a complete discussion.
And
\ =\ \frac{\sqrt{2}}{2})
From the unit circle:
Since the half-angle formula for sine is:
\ =\ \pm\sqrt{\frac{1\ -\ \cos(\varphi)}{2}})
where you select the sign based on the quadrant in which )
exists.
We can write, since 
is in the first quadrant:
\ =\ \sqrt{\frac{1\ -\ \frac{\sqrt{2}}{2}}{2}}\ =\ \frac{\sqrt{2\ -\ \sqrt{2}}}{2})
John
My calculator said it, I believe it, that settles it
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