Questions: Give the degree measure of the angle in the space provided. θ=arcsin(-1/2)

Solution Steps

To find the degree measure of \(\theta = \arcsin\left(-\frac{1}{2}\right)\), we need to determine the angle whose sine is \(-\frac{1}{2}\). The arcsine function returns values in the range \([-90^\circ, 90^\circ]\) or \([- \frac{\pi}{2}, \frac{\pi}{2}]\) in radians. We will use Python to calculate this angle in degrees.

We need to find the angle \( \theta \) such that \( \sin(\theta) = -\frac{1}{2} \). The arcsine function gives us the principal value of the angle in the range \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).

Using the arcsine function, we find: \[ \theta = \arcsin\left(-\frac{1}{2}\right) \approx -0.5236 \text{ radians} \]

To convert the angle from radians to degrees, we use the conversion factor \( \frac{180}{\pi} \): \[ \theta \approx -30.0000^\circ \]

Final Answer