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Answer 1 Using the unit circle, the angle $ \frac{\pi}{3} $ corresponds to 60 degrees. On the unit circle, the coordinates of this angle are:$ \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $The cosine value is the x-coordinate:$ \cos \left(...
Answer 1 To memorize the points on the unit circle, remember that the unit circle has a radius of 1 and is centered at the origin (0,0). The key angles in radians are txt1 txt1 txt1$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$,...
Answer 1 Given a point $(x, y)$ on the unit circle, we know that the equation of the circle is:$ x^2 + y^2 = 1 $If $ x = \frac{1}{2} $, then we can find $ y $ by solving:$ (\frac{1}{2})^2 + y^2 = 1 $$ \frac{1}{4} + y^2 = 1 $Solving for $ y $:$ y^2 =...
Answer 1 To find the arc length of a sector given angle $\theta$ and radius $r$, use the formula: $ L = r \cdot \theta $ In this formula, $L$ is the arc length of the sector, $r$ is the radius of the circle, and $\theta$ is the central angle in...
Answer 1 On the unit circle, the angle $\frac{\pi}{3}$ corresponds to 60 degrees. The coordinates of this point are $(\frac{1}{2}, \frac{\sqrt{3}}{2})$. The x-coordinate of this point is $\cos(\frac{\pi}{3})$.Therefore,$ \cos(\frac{\pi}{3}) =...
Answer 1 To find the exact values of $ \sin $ and $ \cos $ for an angle of 225 degrees using the unit circle, we first convert the angle to radians:$ 225^\circ = 225 \times \frac{\pi}{180} = \frac{5\pi}{4} $The angle \( \frac{5\pi}{4} \) is in the...