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Answer 1 To find the exact values of $ \sin $ and $ \cos $ at $ \theta = \frac{5\pi}{6} $, we use the unit circle.First, find the reference angle:$ \theta_{ref} = \pi - \frac{5\pi}{6} = \frac{\pi}{6} $Using the reference angle $ \frac{\pi}{6} $, we...
Answer 1 Given an angle $ \theta $ on a unit circle, the tangent of the angle is defined as the ratio of the sine to the cosine of the angle.$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $For instance, if $ \theta = \frac{\pi}{4} $:$...
Answer 1 Consider the angles $ \theta = \frac{5\pi}{6} $, $ \theta = \frac{7\pi}{4} $, and $ \theta = \frac{2\pi}{3} $ on the unit circle. We need to find the exact values of $ \sin(\theta) $, $ \cos(\theta) $, and $ \tan(\theta) $ for each angle.For...
Answer 1 To find the sine and cosine values at specific angles on the unit circle, we use the definitions of sine and cosine in terms of the unit circle.For example, at an angle of 30 degrees (or $\frac{\pi}{6}$ radians):$ \sin(\frac{\pi}{6}) =...
Answer 1 To find the value of $\tan(240)$ using the unit circle, we first determine the corresponding point on the unit circle for an angle of 240 degrees. 240 degrees is in the third quadrant, where the tangent function is positive. We can subtract...
Answer 1 To find the coordinates of the point on the unit circle that corresponds to an angle of $\frac{7\pi}{4}$, we use the sine and cosine functions:$x = \cos\left(\frac{7\pi}{4}\right)$$y = \sin\left(\frac{7\pi}{4}\right)$Since $\frac{7\pi}{4}$...