by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the equation of the unit circle centered at the origin. Answer 1 Matthew Carter To find the equation of the unit circle centered at the origin, we start with the standard form of the circle equation:$ (x – h)^2 + (y – k)^2 = r^2 $For a unit...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Determine the angle measures of a point on the unit circle Answer 1 Thomas Walker Given a point $P$ on the unit circle with coordinates $P = (frac{3}{5}, -frac{4}{5})$, determine all possible angle measures $theta$ in degrees.First, we calculate the reference...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Finding Specific Trigonometric Values on the Unit Circle Answer 1 Henry Green Given the angle θ = 225°, find the sine, cosine, and tangent values using the unit circle. First, convert the angle 225° to radians: $225° = frac{5pi}{4}$ radians. On the unit circle,...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the tangent of the angle Answer 1 Charlotte Davis Given an angle ( theta = frac{pi}{4} ), find ( tan(theta) ). Since the angle ( theta ) is within the first quadrant and ( tan(theta) = frac{sin(theta)}{cos(theta)} ), we have: $ sin(frac{pi}{4}) =...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the cotangent of the angle $ heta = frac{pi}{4}$ on the unit circle. Answer 1 Michael Moore To find the cotangent of $theta = frac{pi}{4}$ on the unit circle:The cotangent function is given by:$cot theta = frac{1}{tan theta}$Since $tan theta = frac{sin...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Given a point on the unit circle at an angle of $frac{5pi}{4}$ radians, find the coordinates of this point. Then, if the unit circle is flipped about the y-axis, determine the new coordinates of the original point after the flip. Answer 1 Samuel Scott First, find...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the values of $cot( heta)$ for a given angle on the unit circle and verify their consistency Answer 1 Benjamin Clark To find the values of $cot(theta)$ for $theta = frac{3pi}{4}$ on the unit circle, we start by identifying the coordinates of this angle on...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home What is the cosine of the angle at $ frac{2pi}{3} $ on the unit circle? Answer 1 Amelia Mitchell First, recognize that the angle $ frac{2pi}{3} $ is in the second quadrant.In the unit circle, the cosine function is negative in the second quadrant.The reference...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Determine the Tangent Slope at a Given Point on the Unit Circle Answer 1 Maria Rodriguez Let the given point on the unit circle be $(a, b)$, where $a^2 + b^2 = 1$. We need to determine the slope of the tangent line at this point. The equation of the unit circle...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $Find the value of tan(frac{4pi}{3}) using the unit circle$ Answer 1 Benjamin Clark $To find the value of tan(frac{4pi}{3}) using the unit circle, we first need to determine the reference angle. $ $The angle frac{4pi}{3} is in the third quadrant, and its...