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Answer 1 To find the coordinates of the point on the unit circle at an angle of $ \pi/3 $ , we use the fact that the unit circleAnswer 2 The coordinates on the unit circle at an angle of $ pi/3 $ are determined by $ (cos( heta), sin( heta)) $. For $...
Answer 1 To complete the unit circle, fill in the following values:$\text{1. } \sin(\frac{\pi}{6}) = \frac{1}{2}, \cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$$\text{2. } \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}, \cos(\frac{\pi}{4}) =...
Answer 1 To find the coordinates on the unit circle at an angle of $ \frac{\pi}{3} $, we use the unit circle definition: $ (\cos(\theta), \sin(\theta)) $For $ \theta = \frac{\pi}{3} $:$ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} $$...
Answer 1 First, recognize that $ \sin(\theta) = -\frac{1}{2} $ in the third and fourth quadrants. The angles in these quadrants are $ \theta = \frac{7\pi}{6} $ and $ \theta = \frac{11\pi}{6} $. Next, recognize that $ \cos(\theta) =...
Answer 1 In a right triangle on the unit circle, the hypotenuse is always 1. If one side is $ \frac{1}{\sqrt{2}} $, the other side must also be $ \frac{1}{\sqrt{2}} $ to satisfy the Pythagorean theorem:$ a^2 + b^2 = c^2 $Here, $ a =...
Answer 1 Given the angle $\theta = \frac{\pi}{4}$, the corresponding coordinates on the unit circle are:$ (\cos(\theta), \sin(\theta)) = \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) $Thus,$ \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}...