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Answer 1 To find the value of $ \arctan(\sin(\frac{3\pi}{4})) $, we first need to find the value of $ \sin(\frac{3\pi}{4}) $.$ \sin(\frac{3\pi}{4}) = \sin(\pi - \frac{\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $Now, we need to determine the...
Answer 1 The unit circle is defined as a circle with radius 1 centered at the origin. The coordinates of any point on the unit circle can be given by $(\cos(\theta), \sin(\theta))$ where $\theta$ is the angle with the positive $x$-axis.Given that...
Answer 1 To determine the coordinates where the terminal side of $\theta = \frac{5\pi}{6}$ intersects the unit circle:First, recall that on the unit circle, the coordinates are given by $(\cos(\theta), \sin(\theta))$.Calculate the cosine and sine...
Answer 1 The area of a sector of a circle with radius $ r $ and central angle $ \theta $ can be calculated using the formula:$ A = \frac{1}{2} r^2 \theta $For example, if $ r = 5 $ and $ \theta = \frac{\pi}{3} $:$ A = \frac{1}{2} \cdot 5^2 \cdot...
Answer 1 To determine the exact values of $\sin(\frac{5\pi}{6})$ and $\cos(\frac{5\pi}{6})$, we use the unit circle.For the angle $\frac{5\pi}{6}$, it is in the second quadrant where sine is positive and cosine is negative. The reference angle for...
Answer 1 LetAnswer 2 Consider the point $(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle. This corresponds to the angle $ heta $ where: $ cos( heta) = frac{1}{2} $ $ sin( heta) = frac{sqrt{3}}{2} $ From trigonometric values,: $ heta = frac{pi}{3}...