by zhanhongyuan | Feb 4, 2025 | Math
Home Calculate the integral of $ frac{1}{1 + x^2} $ over the unit circle Answer 1 Benjamin Clark To calculate the integral of $ frac{1}{1 + x^2} $ over the unit circle, we first convert to polar coordinates: $ x = r cos(theta), y = r sin(theta) $ In polar coordinates,...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the cosine and sine values at $ frac{pi}{4} $ on the unit circle Answer 1 Lily Perez 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) =...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the value of $cos( heta)$ and $sin( heta)$ for $ heta=frac{pi}{4}$ on the unit circle Answer 1 Daniel Carter 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...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the value of $ cos( heta) $ and $ sin( heta) $ for $ heta = frac{pi}{4} $ Answer 1 Benjamin Clark 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}...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the value of $ cos(frac{pi}{3}) $ and $ sin(frac{pi}{3}) $ Answer 1 Ava Martin 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},...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Calculate the value of $ sin(2 heta) $ if $ cos( heta) = frac{3}{5} $ and $ heta $ is in the first quadrant Answer 1 Alex Thompson To find the value of $ sin(2theta) $, we use the double angle identity for sine:$ sin(2theta) = 2 sin(theta) cos(theta) $Given that...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the angle on the unit circle corresponding to $ arctanleft(frac{1}{sqrt{3}} ight) $ Answer 1 Henry Green Given $ arctanleft(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...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the cosine of $ frac{pi}{3} $ using the unit circle Answer 1 Michael Moore 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) $The...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home How to memorize the points on the unit circle Answer 1 Ava Martin To memorize the points on the unit circle, remember that the unit circle has a radius of 1 and is centered at the origin (0,0). The key angles in radians are txt1 txt1 txt1$, $frac{pi}{6}$,...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the coordinates of point on the unit circle Answer 1 Mia Harris 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 $$...