Question

Would you be able to find sin 22.5° using the double angle formula, or only the half angle formula?

Answer 1

\[\cos 2A=1-\sin ^2A\]
A=22.45
2A=45
sin 22.5 is positive.

Answer 2

The Half-Angle and Double-Angle are essentially the same thing, just rearranged. If you used the Double-Angle Formula, you would have to move things around and turn it into the Half-Angle to solve properly.

So just stick with Half-Angle Formula for this one :)\[\large\rm \sin(22.5^o)=\sin\left(\frac{45^o}{2}\right)=\sqrt{\frac{1-\cos(45^o)}{2}}\]

Answer 3

Thank you!