What is the value of \(\sin 15°\)?
Answer: B
We can write 15° as the difference of two standard angles, 45° - 30°.
Using the sine subtraction formula: \(\sin(A-B) = \sin A \cos B - \cos A \sin B\).
\(\sin(45°-30°) = \sin 45° \cos 30° - \cos 45° \sin 30°\)
= \((\frac{1}{\sqrt{2}})(\frac{\sqrt{3}}{2}) - (\frac{1}{\sqrt{2}})(\frac{1}{2})\)
= \(\frac{\sqrt{3}}{2\sqrt{2}} - \frac{1}{2\sqrt{2}} = \frac{\sqrt{3}-1}{2\sqrt{2}}\).