Problem 4 - Calculus of a Single Variable

Question

Evaluate the expression without using a calculator. \(\arcsin \frac{1}{2}\)

Step-by-Step Solution

Answer

\(\arcsin \frac{1}{2} = \frac{\pi}{6}\)

Step 1: Recalling Sine Values

By recalling the unit circle in trigonometry, we know the sine of several key angles by heart. We know that \(\sin(\frac{\pi}{6}) = \frac{1}{2}\).

Step 2: Apply Arcsine

The concept of arcsine is the angle of sine. Hence, we find the angle whose sine gives \(\frac{1}{2}\), which we know from Step 1. Thus, \(\arcsin \frac{1}{2} = \frac{\pi}{6}\).