Questions: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) arcsin (1)

Transcript text: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) $\arcsin (1)$

Solution

Solution Steps

To find the exact value of the expression $\arcsin(1)$, we need to determine the angle whose sine is 1. The arcsine function, $\arcsin(x)$, returns the angle in the range $[- \frac{\pi}{2}, \frac{\pi}{2}]$ whose sine is $x$. The sine of $\frac{\pi}{2}$ is 1, so $\arcsin(1) = \frac{\pi}{2}$.

Step 1: Determine the Angle

To find the value of $\arcsin(1)$, we need to identify the angle $\theta$ such that $\sin(\theta) = 1$. The sine function reaches its maximum value of 1 at $\theta = \frac{\pi}{2}$.

Step 2: Calculate the Value

Using the properties of the arcsine function, we find that: \[ \arcsin(1) = \frac{\pi}{2} \]

Step 3: Present the Result

The exact value of the expression $\arcsin(1)$ is $\frac{\pi}{2}$.