Questions: Find the exact value or state that the expression is undefined. arcsin(sqrt(2)/2) =

Solution Steps

To find the exact value of \(\arcsin \frac{\sqrt{2}}{2}\), we need to determine the angle whose sine is \(\frac{\sqrt{2}}{2}\). This is a common trigonometric value, and the angle is known to be \(\frac{\pi}{4}\) or \(45^\circ\). Since \(\arcsin\) returns values in the range \([- \frac{\pi}{2}, \frac{\pi}{2}]\), the correct answer is \(\frac{\pi}{4}\).

To find the value of \(\arcsin \frac{\sqrt{2}}{2}\), we need to identify the angle \(\theta\) such that \(\sin \theta = \frac{\sqrt{2}}{2}\). The angle that satisfies this equation is \(\theta = \frac{\pi}{4}\).

The value of \(\frac{\pi}{4}\) in decimal form is approximately \(0.7854\).

The result can also be expressed as a fraction of \(\pi\): \[ \frac{\pi}{4} \approx 0.2500 \text{ (when expressed as a fraction of } \pi\text{)} \]

Final Answer