by zhanhongyuan | Feb 6, 2025 | Math
Home Find the equation of the circle passing through the points $ (1,2) $, $ (3, -4) $, and $ (5, 6) $. Answer 1 Ava Martin To find the equation of the circle passing through three points, we use the general form of the equation of a circle: $ (x – h)^2 + (y...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Calculate the coordinates of a point on the unit circle, given $ heta$ in radians. Answer 1 Daniel Carter To calculate the coordinates of a point on the unit circle given an angle $theta$ in radians, use the formulas: $ x = cos(theta) $ and $ y = sin(theta) $ For...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the coordinates where the function $ f( heta) = sin(2 heta) $ intersects with the unit circle Answer 1 Matthew Carter To find the coordinates where $ f(theta) = sin(2theta) $ intersects the unit circle, we start by setting $ sin(2theta) = y $.The unit circle...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the sine and cosine values at $ frac{pi}{3} $ Answer 1 Daniel Carter To find the sine and cosine values at $ frac{pi}{3} $:nThe unit circle values for $ frac{pi}{3} $ are:n$ sin left( frac{pi}{3} right) = frac{sqrt{3}}{2} $n$ cos left( frac{pi}{3} right) =...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the cosine of $ heta $ if $ sin( heta) = frac{1}{2} $ and $ heta $ is in the first quadrant Answer 1 Thomas Walker Given $ sin(theta) = frac{1}{2} $ and $ theta $ is in the first quadrant.We know that $ sin^2(theta) + cos^2(theta) = 1 $.So,$ left( frac{1}{2}...
by zhanhongyuan | Feb 6, 2025 | Math
Home Identify the quadrant of the angle $ heta = frac{pi}{3} $ Answer 1 Sophia Williams To determine the quadrant of the angle $ theta = frac{pi}{3} $, we convert it to degrees:$ theta = frac{pi}{3} times frac{180}{pi} = 60^{circ} $The angle $ 60^{circ} $ lies in the...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Calculate the exact values of the trigonometric functions for an angle of $ frac{7pi}{6} $ radians on the unit circle. Answer 1 Matthew Carter To find the trigonometric functions for the angle $ frac{7pi}{6} $, locate the angle on the unit circle.First, convert $...
by zhanhongyuan | Feb 6, 2025 | Math
Home Find the coordinates of points on the unit circle corresponding to specific angles $ heta = frac{pi}{6}, heta = frac{pi}{4}, heta = frac{pi}{3} $ Answer 1 John Anderson To find the coordinates of points on the unit circle corresponding to $ theta = frac{pi}{6},...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the tangent value of $ frac{pi}{4} $ in the unit circle Answer 1 Sophia Williams To find the tangent value of $ frac{pi}{4} $ in the unit circle, use the definition of tangent:$ tan(theta) = frac{sin(theta)}{cos(theta)} $At $ theta = frac{pi}{4} $, both the...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the point(s) where the derivative of $ cos( heta) $ equals zero on the filled out unit circle Answer 1 Charlotte Davis To find where the derivative of $ cos(theta) $ equals zero, we first need to find the derivative: $ frac{d}{dtheta} cos(theta) =...