by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the value of trigonometric functions at $frac{pi}{3}$ on the unit circle Answer 1 James Taylor To find the value of trigonometric functions at $frac{pi}{3}$ on the unit circle, we need to calculate $sinleft(frac{pi}{3}right)$ and...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the angle $ heta $ on the unit circle where the equation $ cos^2( heta) - sin^2( heta) = 1 - 2sin^2( heta) $ holds true Answer 1 Benjamin Clark To solve for $ theta $ on the unit circle in the equation $ cos^2(theta) – sin^2(theta) = 1 –...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the exact values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ at $ heta = frac{3pi}{4} $ Answer 1 Emily Hall To find the exact values of $ sin(theta) $, $ cos(theta) $, and $ tan(theta) $ at $ theta = frac{3pi}{4} $, we use the unit circle:For $...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the exact coordinates of the point where the angle $ frac{7pi}{6} $ intersects the unit circle Answer 1 Thomas Walker To find the coordinates of the point where the angle $ frac{7pi}{6} $ intersects the unit circle, we first identify the reference angle. The...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Draw a point on the unit circle at angle $ frac{pi}{4} $ Answer 1 John Anderson The unit circle has a radius of 1. To draw a point at angle $ frac{pi}{4} $, use the coordinates:$ (cos(frac{pi}{4}), sin(frac{pi}{4})) $Since $ cos(frac{pi}{4}) = sin(frac{pi}{4}) =...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the coordinates of the point where the terminal side of $ heta $ intersects the unit circle at $ heta = frac{5pi}{6} $ Answer 1 James Taylor To find the coordinates of the point where the terminal side of $ theta $ intersects the unit circle at $ theta =...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home What is a unit circle in trigonometry, and how is it used to define the trigonometric functions? Answer 1 Sophia Williams A unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. The equation of the unit circle is given...
by zhanhongyuan | Feb 7, 2025 | Math
Home Calculate the circumference of a circle given its radius in different units Answer 1 Amelia Mitchell To calculate the circumference of a circle, we use the formula:$ C = 2pi r $If the radius $r$ is given in meters (m), and the radius is 5 meters, then the...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the sine value for $ frac{5pi}{6} $ on the unit circle Answer 1 Lily Perez To find the sine value for $ frac{5pi}{6} $ on the unit circle, we follow these steps:First, understand that $ frac{5pi}{6} $ is in the second quadrant.The reference angle is $ pi...
by zhanhongyuan | Feb 7, 2025 | Unit Circle
Home Find the value of $sin$ and $cos$ for specific angles using the unit circle Answer 1 Isabella Walker Using the unit circle, find the values of $sin$ and $cos$ for the angle $frac{pi}{4}$. For $theta = frac{pi}{4}$: $sinleft(frac{pi}{4}right) = frac{sqrt{2}}{2}$...