by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Create a colorful circle pattern using points on the unit circle with $cos( heta)$ and $sin( heta)$ Answer 1 John Anderson To create a colorful circle pattern, you can use points on the unit circle defined by $cos(theta)$ and $sin(theta)$ where txt1 txt1 txt1 leq...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the coordinates on the unit circle for the angle $-frac{2}{3}π$ Answer 1 Ava Martin To determine the coordinates on the unit circle for the angle $-frac{2}{3}π$, we first convert this angle to its corresponding positive angle by adding $2π$:$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $ arcsin(frac{1}{2}) $. Answer 1 Ava Martin To find the value of $ arcsin(frac{1}{2}) $, we need to determine the angle $ theta $ whose sine is $ frac{1}{2} $.From the unit circle, we know:$ sin(theta) = frac{1}{2} $The angle $ theta $ that...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the coordinates on the unit circle corresponding to an angle $ heta $ Answer 1 Daniel Carter To find the coordinates on the unit circle corresponding to an angle $ theta $ , we use the parametric equations of the unit circle:$ x = cos(theta) $$ y =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home How to find the reference angle for an angle not located on the unit circle Answer 1 Charlotte Davis To find the reference angle for an angle not located on the unit circle, we first need to understand that the reference angle is the smallest angle between the...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home What is the value of $cos(-frac{pi}{3})$ using the unit circle? Answer 1 Abigail Nelson To find the value of $cos(-frac{pi}{3})$ using the unit circle, first recognize that the cosine function is an even function. This means that:$cos(-x) =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle at which the angle is $ frac{7pi}{6} $ Answer 1 Lily Perez To find the coordinates of the point on the unit circle at which the angle is $ frac{7pi}{6} $, we use the following:The unit circle has the equation:$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the exact coordinates of the point(s) on the unit circle where the tangent line is vertical Answer 1 Lucas Brown The equation of the unit circle is given by:$ x^2 + y^2 = 1 $We find the tangent line to be vertical when the derivative is undefined. Thus, we...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the sine and cosine of the angle when the point is ( left( frac{1}{2}, frac{sqrt{3}}{2} ight) ) on the unit circle Answer 1 Lucas Brown The coordinates ( left( frac{1}{2}, frac{sqrt{3}}{2} right) ) on the unit circle represent the cosine and sine of an...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the integral of $ sin(x) * cos(x) $ around the unit circle Answer 1 Sophia Williams To evaluate the integral of $ sin(x) * cos(x) $ around the unit circle, we can use the double-angle identity: $ sin(x) cos(x) = frac{1}{2} sin(2x) $Now, we need to...