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Answer 1 To find the cosine and sine values at $ \frac{\pi}{4} $ on the unit circle:$ \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $ $ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $The values are:$ \cos \left( \frac{\pi}{4}...
Answer 1 To determine the values of $\cos(\theta)$ and $\sin(\theta)$ for $\theta=\frac{\pi}{4}$ on the unit circle, we use the known coordinates:At $\theta=\frac{\pi}{4}$, both cosine and sine values are equal to:$\cos\left(\frac{\pi}{4}\right) =...
Answer 1 To find the values of $ \cos(\theta) $ and $ \sin(\theta) $ when $ \theta = \frac{\pi}{4} $, we use the unit circle.On the unit circle, when $ \theta = \frac{\pi}{4} $, both $ \cos(\theta) $ and $ \sin(\theta) $ are equal to:$...
Answer 1 To find the value of $ \cos(\frac{\pi}{3}) $, we look at the coordinates of the corresponding point on the unit circle.The coordinate point at $ \frac{\pi}{3} $ is $ (\frac{1}{2}, \frac{\sqrt{3}}{2}) $.Hence, $ \cos(\frac{\pi}{3}) =...
Answer 1 To find the value of $ \sin(2\theta) $, we use the double angle identity for sine:$ \sin(2\theta) = 2 \sin(\theta) \cos(\theta) $Given that $ \cos(\theta) = \frac{3}{5} $, we need to find $ \sin(\theta) $. Since $ \theta $ is in the first...
Answer 1 Given $ \arctan\left(\frac{1}{\sqrt{3}}\right) $, we need to determine the angle $ \theta $ on the unit circle.We know that $ \arctan(x) $ gives the angle whose tangent is $ x $. Hence:$ \tan(\theta) = \frac{1}{\sqrt{3}} $We recognize that...