by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the values of $ heta $ for which $ an( heta) = 1 $ in the unit circle Answer 1 Daniel Carter To find the values of $ theta $ for which $ tan(theta) = 1 $ on the unit circle, we need to identify the angles where the tangent function is equal to 1.The tangent...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the exact values of the trigonometric functions for the angle $ frac{5pi}{3} $ in the unit circle Answer 1 Sophia Williams To find the exact values of the trigonometric functions for the angle $ frac{5pi}{3} $ in the unit circle, we first note that:$...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Identify the location of $-pi/2$ on a unit circle Answer 1 Chloe Evans On the unit circle, angles are measured starting from the positive x-axis and moving counterclockwise.To find the location of $-pi/2$:- Starting from the positive x-axis, move clockwise...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the value of $ heta $ for which the point $ (cos( heta), sin( heta)) $ on the unit circle forms a right-angled triangle with the origin and the point $ (1, 0) $ Answer 1 William King Given the points $ (cos(theta), sin(theta))$, the origin $(0, 0)$, and...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Calculate the area of a sector in a unit circle with a given central angle $ heta $. Answer 1 Maria Rodriguez To calculate the area of a sector in a unit circle with a given central angle $ theta $ (in radians), use the following formula: $ A = frac{1}{2} cdot...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the values of $ an( heta)$, $sin( heta)$, and $cos( heta)$ for $ heta = 45^circ$ Answer 1 Thomas Walker To find the values of $tan(theta)$, $sin(theta)$, and $cos(theta)$ for $theta = 45^circ$:First, we note that $theta = 45^circ$ is in the first quadrant of...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Prove the identity involving $cos( heta)$ and $sin( heta)$ on the unit circle Answer 1 Ava Martin To prove the identity involving $ cos(theta) $ and $ sin(theta) $ on the unit circle, we start with the Pythagorean identity:$ cos^2(theta) + sin^2(theta) = 1...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the coordinates of the point where the line $ y = 1 $ intersects the unit circle Answer 1 Emily Hall To find the coordinates where the line $ y = 1 $ intersects the unit circle, we start by recalling the equation of the unit circle:$ x^2 + y^2 = 1...
by zhanhongyuan | Feb 6, 2025 | Math
Home Determine the equation of the tangent line to the unit circle at the point $ left( frac{1}{2}, frac{sqrt{3}}{2} ight) $ Answer 1 Christopher Garcia The equation of the unit circle is given by: $ x^2 + y^2 = 1 $ To find the tangent line at the point $left(...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the exact values of $ sin $, $ cos $, and $ an $ at $ 30^{circ} $ on the unit circle Answer 1 Abigail Nelson First, we need to convert $ 30^{circ} $ to radians: $ 30^{circ} = frac{pi}{6} $ Using the unit circle, the coordinates for $ frac{pi}{6} $ are $...