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Answer 1 The equation of a unit circle centered at the origin is given by:$ x^2 + y^2 = 1 $This equation signifies that any point $ (x, y) $ on the unit circle is at a distance of 1 unit from the origin. The radius of the circle is always 1.Answer 2...
Answer 1 We need to find the value of $ \tan(\theta) $ where $ \theta = \frac{3\pi}{4} $ using the unit circle. The coordinates of the point on the unit circle corresponding to $ \theta = \frac{3\pi}{4} $ are:$ \left( -\frac{\sqrt{2}}{2},...
Answer 1 To determine the trigonometric identity of $ \sin(\theta) $ using the unit circle, we start by understanding the unit circle definition:The unit circle is a circle with a radius of $1$ centered at the origin $(0, 0)$.For any angle $\theta$...
Answer 1 To find the values of $ \sin(\theta) $, $ \cos(\theta) $, and $ \tan(\theta) $ for $ \theta = \frac{7\pi}{6} $ using the unit circle, we start by locating the angle on the unit circle:$ \theta = \frac{7\pi}{6} $ corresponds to an angle in...
Answer 1 To find the value of $ \cos(\theta) $ on the Unit Circle at specific points, consider the following:When $ \theta = 0 $:$ \cos(0) = 1 $When $ \theta = \frac{\pi}{2} $:$ \cos\left(\frac{\pi}{2}\right) = 0 $When $ \theta = \pi $:$ \cos(\pi) =...
Answer 1 To find the values of $ \sin(x) = 0.5 $ on the unit circle, we need to determine the angles where the sine function equals 0.5. From the unit circle, we know that:$ \sin(\frac{\pi}{6}) = 0.5 $$ \sin(\frac{5\pi}{6}) = 0.5 $So the values of...