by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home What are some effective methods to memorize the angles and coordinates on the unit circle? Answer 1 Michael Moore One effective method to memorize the unit circle is to understand the symmetries in the circle. The unit circle is symmetrical across the x-axis,...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Calculate the exact values of $ sin $ and $ cos $ at $ heta = frac{5pi}{6} $ Answer 1 John Anderson To find the exact values of $ sin $ and $ cos $ at $ theta = frac{5pi}{6} $, we use the unit circle.First, find the reference angle:$ theta_{ref} = pi –...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the tangent of an angle $ heta $ on a unit circle Answer 1 Christopher Garcia Given an angle $ theta $ on a unit circle, the tangent of the angle is defined as the ratio of the sine to the cosine of the angle.$ tan(theta) = frac{sin(theta)}{cos(theta)} $For...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the exact values of trigonometric functions at angles on the unit circle Answer 1 Alex Thompson Consider the angles $ theta = frac{5pi}{6} $, $ theta = frac{7pi}{4} $, and $ theta = frac{2pi}{3} $ on the unit circle. We need to find the exact values of $...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the sine and cosine values at specific angles on the unit circle Answer 1 Maria Rodriguez To find the sine and cosine values at specific angles on the unit circle, we use the definitions of sine and cosine in terms of the unit circle.For example, at an angle...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the value of $ an(240)$ using the unit circle Answer 1 Samuel Scott To find the value of $tan(240)$ using the unit circle, we first determine the corresponding point on the unit circle for an angle of 240 degrees. 240 degrees is in the third quadrant, where...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle that corresponds to an angle of $frac{7pi}{4}$ Answer 1 Samuel Scott To find the coordinates of the point on the unit circle that corresponds to an angle of $frac{7pi}{4}$, we use the sine and cosine functions:$x...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the derivative of $ cos(x^2) $ with respect to $ x $ Answer 1 Christopher Garcia To find the derivative of $ cos(x^2) $ with respect to $ x $, we use the chain rule:n$ frac{d}{dx} cos(u) = -sin(u) cdot frac{du}{dx} $nHere, let $ u = x^2 $. Then:n$...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the tangent values for the primary angles on the unit circle Answer 1 Olivia Lee To determine the tangent values for the primary angles on the unit circle, we need to evaluate the tangent function at txt1 txt1 txt1, frac{pi}{6}, frac{pi}{4},...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home How to find $sin$, $cos$, and $ an$ for an angle using the unit circle? Answer 1 James Taylor To find the sine, cosine, and tangent of an angle using the unit circle, follow these steps:1. Locate the angle on the unit circle.2. Identify the coordinates $(x, y)$...