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Answer 1 At the angle $ \frac{\pi}{4} $, the coordinates on the unit circle are: $ \left( \cos\left( \frac{\pi}{4} \right), \sin\left( \frac{\pi}{4} \right) \right) $ Using the unit circle values: $ \cos\left( \frac{\pi}{4} \right) =...
Answer 1 To determine the quadrant of an angle $ \theta $ in radians on the unit circle, follow these steps:1. If $ \theta $ is greater than $ 2\pi $ or less than $ -2\pi $, reduce it by subtracting or adding multiples of $ 2\pi $ until it is within...
Answer 1 To determine the quadrant of an angle of $45^{\circ}$, we need to look at the unit circle. Angles are measured counterclockwise from the positive x-axis.Since $45^{\circ}$ is between txt1 txt1 txt1^{\circ}$ and $90^{\circ}$, it lies in the...
Answer 1 To find the probability density function (pdf) for a uniform distribution on the unit circle, we start by noting that the unit circle can be expressed in terms of its angular coordinate $\theta$, where txt1 txt1 txt1 \leq \theta <...
Answer 1 To find the reference angle for $ \frac{5\pi}{3} $ radians, we need to determine its corresponding acute angle in the first quadrant.\nFirst, convert $ \frac{5\pi}{3} $ to degrees:\n$ \frac{5\pi}{3} \times \frac{180^\circ}{\pi} = 300^\circ...
Answer 1 To find the equation of the tangent line to the unit circle at the point $(a,b)$, recall that the unit circle is given by:$ x^2 + y^2 = 1 $Since the radius at the point $(a,b)$ is perpendicular to the tangent, the slope of the radius is:$...