\( \sin 45^{\circ} \cos 60^{\circ}+\cos 60^{\circ} \sin 45^{\circ}=\ldots \) a. 1

Did you know that \( \sin 45^{\circ} \) and \( \cos 60^{\circ} \) both have standard values found in the unit circle? Specifically, \( \sin 45^{\circ} = \frac{\sqrt{2}}{2} \) and \( \cos 60^{\circ} = \frac{1}{2} \). When you plug these values into the equation, you can simplify the expression easily! Now, this expression is a classic example of the angle sum identity for sine! It can be rewritten as \( \sin(45^{\circ} + 60^{\circ}) \). So, you can actually find that \( \sin(105^{\circ}) \) equals \( \frac{\sqrt{3}}{2} \) by using the known values of sine and cosine for 30, 60, and 90 degrees.