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Answer 1 To find the coordinates of the point at an angle of $ \frac{\pi}{3} $ on the unit circle, we use the unit circle definition where the coordinates are given by $ (\cos\theta, \sin\theta) $.For $ \theta = \frac{\pi}{3} $, we have:$ \cos \left(...
Answer 1 Given $\theta = \frac{5\pi}{4}$, we determine the sine and cosine values by examining the unit circle. The angle $\frac{5\pi}{4}$ is located in the third quadrant, where sine and cosine values are negative. Specifically:$ \sin \left(...
Answer 1 Consider the point $P(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$ on the unit circle. Determine the exact values for the following inverse trigonometric functions:1. $\arcsin(-\frac{\sqrt{3}}{2})$2. $\arccos(-\frac{1}{2})$3....
Answer 1 To find the value of $ \tan(θ) $ at $ θ = \frac{3π}{4} $, we first identify the coordinates on the unit circle:At $ θ = \frac{3π}{4} $, the coordinates are $ (-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) $.So, $ \tan(θ) $ is given by:$ \tan(θ) =...
Answer 1 First, locate the angle $\frac{7\pi}{6}$ on the unit circle. This angle corresponds to 210 degrees. The coordinates of the point on the unit circle at this angle are: $ \left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right) $ Thus: $...
Answer 1 To find the values of $\cos(x) = -\frac{1}{2}$ on the unit circle, we start by considering the unit circle where $\cos(\theta)$ is the x-coordinate of the point corresponding to the angle $\theta$:\n$ \cos(x) = -\frac{1}{2} $\nWe know from...