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Answer 1 To determine the sine value at an angle of $ \frac{\pi}{4} $ on the unit circle, recall that at this angle, the coordinates are:$ ( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} ) $The sine value corresponds to the y-coordinate:$ \sin(...
Answer 1 To determine $ \tan(\theta) $ from the unit circle at point $ P(x,y) $, recall that$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $On the unit circle, you have $ P(x,y) = (\cos(\theta), \sin(\theta)) $, so$ \tan(\theta) = \frac{y}{x}...
Answer 1 To create a colorful circle pattern, you can use points on the unit circle defined by $\cos(\theta)$ and $\sin(\theta)$ where txt1 txt1 txt1 \leq \theta \leq 2\pi$. Each point coordinates can be calculated as:$ x = \cos(\theta) $$ y =...
Answer 1 To determine the coordinates on the unit circle for the angle $-\frac{2}{3}π$, we first convert this angle to its corresponding positive angle by adding $2π$:$ -\frac{2}{3}π + 2π = \frac{4π}{3} $Now, we find the coordinates corresponding to...
Answer 1 To find the value of $ \arcsin(\frac{1}{2}) $, we need to determine the angle $ \theta $ whose sine is $ \frac{1}{2} $.From the unit circle, we know:$ \sin(\theta) = \frac{1}{2} $The angle $ \theta $ that satisfies this in the range $...
Answer 1 To find the coordinates on the unit circle corresponding to an angle $ \theta $ , we use the parametric equations of the unit circle:$ x = \cos(\theta) $$ y = \sin(\theta) $Thus, the coordinates are given by:$ (x, y) = (\cos(\theta),...