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Answer 1 To determine the value of $ \tan(\theta) $ at $ \theta = \frac{3\pi}{4} $, we use the unit circle chart. The angle $ \frac{3\pi}{4} $ is in the second quadrant, where the reference angle is $ \frac{\pi}{4} $. In this quadrant, the tangent...
Answer 1 The unit circle has a radius of 1. The coordinates of a point on the circle at angle $ \frac{\pi}{3} $ are given by:$ (\cos(\frac{\pi}{3}), \sin(\frac{\pi}{3})) $Therefore,$ \cos(\frac{\pi}{3}) = \frac{1}{2} $and$ \sin(\frac{\pi}{3}) =...
Answer 1 In the second quadrant, the angle $ \theta $ ranges from $ \frac{\pi}{2} $ to $ \pi $. Here, $ \sin(\theta) $ is positive, $ \cos(\theta) $ is negative, and $ \tan(\theta) $ is negative.Using the unit circle, for $ \theta = \frac{2\pi}{3}...
Answer 1 To find the value of $ \sin\left(\frac{\pi}{3}\right) $ on the unit circle, we look at the reference angle for $ \frac{\pi}{3} $.The reference angle is $ 60^{\circ} $, and the sine value for $ 60^{\circ} $ is:$ \sin\left(60^{\circ}\right) =...
Answer 1 To find the area of a sector of a unit circle with a central angle of $ \theta $, we use the formula for the area of a sector:\n$ A = \frac{1}{2} r^2 \theta $\nSince the radius $ r $ of a unit circle is 1, the formula simplifies to:\n$ A =...
Answer 1 Using the unit circle chart, we find:$ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} $$ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} $$ \tan\left(\frac{\pi}{4}\right) = 1 $Answer 2 From the unit circle:$ sinleft(frac{pi}{6} ight) = frac{1}{2}...