Find the solutions to $ arcsin(x) = frac{pi}{6} $ using the unit circle

Answer 1

To find the solutions for $ \arcsin(x) = \frac{\pi}{6} $ using the unit circle, we need to identify the values of $x$ for which the angle is $ \frac{\pi}{6} $:

• On the unit circle, $ \arcsin(x) = \frac{\pi}{6} $ corresponds to the $y$-coordinate of the point where the angle from the positive $x$-axis is $ \frac{\pi}{6} $.
• At $ \frac{\pi}{6} $, the coordinates are $(\frac{\sqrt{3}}{2}, \frac{1}{2})$.
• Thus, $x = \frac{1}{2}$.

Therefore, the solution is:

$ x = \frac{1}{2} $

Answer 2

To solve $ arcsin(x) = frac{pi}{6} $ using the unit circle, consider the $y$-coordinate of the point where the angle from the positive $x$-axis is $ frac{pi}{6} $.

At $ frac{pi}{6} $, the coordinates are $(frac{sqrt{3}}{2}, frac{1}{2})$, so:

$ x = frac{1}{2} $

Answer 3

Using the unit circle, for $ arcsin(x) = frac{pi}{6} $, the $y$-coordinate is $ frac{1}{2} $:

$ x = frac{1}{2} $

Start Using PopAi Today