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Answer 1 In the unit circle, when $ \sin(\theta) = \frac{1}{2} $, we need to determine $ \cos(\theta) $.Since $ \sin(\theta) $ relates to the y-coordinate and $ \cos(\theta) $ relates to the x-coordinate in the unit circle, we use the Pythagorean...
Answer 1 The unit circle is defined as the set of points (x,y) such that $x^2 + y^2 = 1$. For a point on the unit circle at an angle $ \theta $, the coordinates of the point are $(\cos(\theta),\sin(\theta))$. For example, if $ \theta = \frac{\pi}{4}...
Answer 1 To find the values of $\cos(\theta)$ and $\sin(\theta)$ when $\theta$ is an angle on the unit circle, we use the coordinates of the corresponding point on the unit circle.\nFor example, if $\theta = \frac{5\pi}{6}$, then the point on the...
Answer 1 One effective method to memorize the unit circle is to understand the symmetries in the circle. The unit circle is symmetrical across the x-axis, y-axis, and the origin. Hence, if you memorize one quadrant, you can derive the other quadrants...
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} $:$...