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Answer 1 We start by noting that $ \frac{3\pi}{4} $ is in the second quadrant of the unit circle.In the second quadrant, the sine value is positive, so we have:$ \sin \left( \frac{3\pi}{4} \right) = \sin( \pi - \frac{\pi}{4}) = \sin \left(...
Answer 1 To find the exact value of $ \text{arcsec}(2) $, we need to determine the angle $ \theta $ such that $ \sec(\theta) = 2 $ and $ \theta $ lies within the range of secantAnswer 2 To determine the value of $ ext{arcsec}(2) $, we need to find...
Answer 1 To find $ \sin(\theta) $ and $ \cos(\theta) $ when $ \theta $ is on the unit circle: Recall the unit circle definition: the unit circle is a circle with a radius of 1 centered at the origin. Therefore, if $ (x, y) $ is a point on the unit...
Answer 1 To find the angles $ \theta $ such that $ \sin(\theta) = \frac{1}{2} $, we need to locate where the y-coordinate on the unit circle is $ \frac{1}{2} $. The angles that satisfy this condition are: $ \theta = \frac{\pi}{6} + 2k\pi $ and $...
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Answer 1 To calculate $ \tan(\theta) $ at $ \theta = 45° $ using the unit circle, we note that at $ 45° $, the coordinates on the unit circle are $ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $.The formula for $ \tan(\theta) $ is:$...