by zhanhongyuan | Feb 4, 2025 | Math
Home Find the arc length of a sector given angle $ heta$ and radius $r$ Answer 1 Benjamin Clark To find the arc length of a sector given angle $theta$ and radius $r$, use the formula: $ L = r cdot theta $ In this formula, $L$ is the arc length of the sector, $r$ is...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the value of $cos(frac{pi}{3})$ using the unit circle on a graphing calculator Answer 1 Maria Rodriguez On the unit circle, the angle $frac{pi}{3}$ corresponds to 60 degrees. The coordinates of this point are $(frac{1}{2}, frac{sqrt{3}}{2})$. The...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the exact values of $ sin $ and $ cos $ for an angle of 225 degrees using the unit circle. Answer 1 Samuel Scott To find the exact values of $ sin $ and $ cos $ for an angle of 225 degrees using the unit circle, we first convert the angle to radians:$...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the sine and cosine of $ frac{pi}{4} $ using the unit circle. Answer 1 Matthew Carter To find the sine and cosine of $ frac{pi}{4} $ using the unit circle:On the unit circle, the angle $ frac{pi}{4} $ corresponds to the coordinates $ left( frac{sqrt{2}}{2},...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle at an angle of ( frac{pi}{4} ) Answer 1 Michael Moore To find the coordinates of a point on the unit circle at an angle of ( frac{pi}{4} ), we use the unit circle definition:n The unit circle is defined as...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the tangent of angle $ heta $ on a unit circle Answer 1 Lily Perez To find the tangent of the angle $ theta $ on a unit circle, one must understand that the tangent of an angle is defined as the ratio of the sine to the cosine of that angle: $ tan(theta) =...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the values of $sin$, $cos$, and $ an$ for angles that satisfy the equation $2sin(x)cos(x) = 1$ Answer 1 Emily Hall First, recognize that $2sin(x)cos(x) = sin(2x)$. Thus, the equation becomes: $sin(2x) = 1$ The solution for $sin(2x) = 1$ occurs at: $2x =...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the coordinates of a point on the negative unit circle given a specific angle $ heta $ Answer 1 Joseph Robinson To find the coordinates of a point on the negative unit circle given a specific angle $ theta $, we use the equation of the unit circle: $ x^2 +...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the points on the negative unit circle where the tangent line is vertical Answer 1 Michael Moore The negative unit circle is described by the equation:$ x^2 + y^2 = -1 $To find where the tangent line is vertical, we need to find the points where the...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Prove that the sum of the squares of the $sin$ and $cos$ functions on the unit circle equals 1. Answer 1 Samuel Scott On the unit circle, any point is represented as $(cos(theta), sin(theta))$, where $theta$ is the angle formed with the positive x-axis.According...