by zhanhongyuan | Feb 5, 2025 | Math
Home Find the equation of the tangent line to the circle at a given point $(3, 4)$ if the equation of the circle is $x^2 + y^2 = 25$ Answer 1 Ava Martin To find the equation of the tangent line to the circle at the point $(3, 4)$, follow these steps:nThe equation of...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the angle $ heta $ in degrees for which the point $ (cos( heta), sin( heta)) $ is closest to the point $ left(frac{1}{2}, -frac{sqrt{3}}{2} ight) $ on the unit circle. Answer 1 Matthew Carter To find θ in degrees, we first find the angle whose...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the secant of the angle when the point on the unit circle is at $ left(frac{sqrt{3}}{2}, frac{1}{2} ight) $ Answer 1 Benjamin Clark Given the point $ left(frac{sqrt{3}}{2}, frac{1}{2}right) $ on the unit circle, we need to find the secant of the...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle with an angle of $ frac{pi}{4} $ Answer 1 Amelia Mitchell The unit circle is a circle with a radius of 1 centered at the origin (0, 0). The coordinates of a point on the unit circle with an angle $...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the exact values of $ sin(x) $, $ cos(x) $, and $ an(x) $ for $ x = frac{7pi}{6} $ using the unit circle. Answer 1 Henry Green To find the exact values of $ sin(x) $, $ cos(x) $, and $ tan(x) $ for $ x = frac{7pi}{6} $, follow these steps:The angle $...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the sine and cosine values at the angle $ frac{pi}{4} $ Answer 1 Isabella Walker At the angle $ frac{pi}{4} $, the coordinates on the unit circle are: $ left( cosleft( frac{pi}{4} right), sinleft( frac{pi}{4} right) right) $ Using the unit circle values: $...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the quadrant of a given angle in radians on the unit circle Answer 1 Thomas Walker To determine the quadrant of an angle $ theta $ in radians on the unit circle, follow these steps:1. If $ theta $ is greater than $ 2pi $ or less than $ -2pi $, reduce it...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the quadrant of an angle of $45^{circ}$ Answer 1 Chloe Evans To determine the quadrant of an angle of $45^{circ}$, we need to look at the unit circle. Angles are measured counterclockwise from the positive x-axis.Since $45^{circ}$ is between txt1 txt1...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the probability density function (pdf) for a uniform distribution on the unit circle. Answer 1 Olivia Lee To find the probability density function (pdf) for a uniform distribution on the unit circle, we start by noting that the unit circle can be expressed...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the reference angle for $ frac{5pi}{3} $ radians and express it in degrees and radians Answer 1 Thomas Walker To find the reference angle for $ frac{5pi}{3} $ radians, we need to determine its corresponding acute angle in the first quadrant.nFirst,...