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Answer 1 To find the coordinates of the point on the unit circle where the angle is $\frac{5\pi}{6}$, we use the unit circle trigonometric identities for sine and cosine. Since $\frac{5\pi}{6}$ is in the second quadrant: The x-coordinate is: $ x =...
Answer 1 To find the coordinates on the unit circle for an angle of $ \frac{\pi}{3} $, we use the cosine and sine functions:$ x = \cos(\frac{\pi}{3}) $$ y = \sin(\frac{\pi}{3}) $The values are:$ \cos(\frac{\pi}{3}) = \frac{1}{2} $$...
Answer 1 To find the coordinates of the point on the unit circle for an angle of $ \frac{3\pi}{4} $ radians, we need to use the unit circle definition:For an angle $ \theta $, the coordinates are given by:$ (\cos(\theta), \sin(\theta)) $ Here, $...
Answer 1 To determine the value of $\cos(\frac{\pi}{4})$, we use the unit circle. At the angle $\frac{\pi}{4}$, the coordinates on the unit circle are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.Since the x-coordinate represents the cosine value, we...
Answer 1 To find the values of $\sin(\frac{\pi}{3})$, $\cos(\frac{\pi}{3})$, and $\tan(\frac{\pi}{3})$, we use the unit circle. For $\theta = \frac{\pi}{3}$: $ \sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2} $ $ \cos(\frac{\pi}{3}) = \frac{1}{2} $ $...
Answer 1 To calculate the integral of $ \frac{1}{1 + x^2} $ over the unit circle, we first convert to polar coordinates: $ x = r \cos(\theta), y = r \sin(\theta) $ In polar coordinates, the unit circle is defined as: $ r = 1 $ Substituting in the...