by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $sin(θ)$, $cos(θ)$, and $ an(θ)$ for $θ = fracπ3$ on the unit circle Answer 1 Charlotte Davis When $θ = fracπ3$, we can find the values of $sin(θ)$, $cos(θ)$, and $tan(θ)$ from the unit circle:$sin(fracπ3) = frac{sqrt3}2$$cos(fracπ3) =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the integral of $ cos(2x) $ from $ 0 $ to $ frac{pi}{2} $ Answer 1 Charlotte Davis To evaluate the integral of $ cos(2x) $ from $ 0 $ to $ frac{pi}{2} $:$ int_0^{frac{pi}{2}} cos(2x) , dx $Use the substitution $ u = 2x $, then $ du = 2dx $ or $ dx =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the coordinates of the point on the unit circle corresponding to a given angle $ heta$ Answer 1 Maria Rodriguez To determine the coordinates of the point on the unit circle corresponding to the angle $theta$, we use the following formulas for the unit...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Identify the coordinates of the point on the unit circle at an angle of $ frac{pi}{4} $ Answer 1 Lily Perez On the unit circle, the coordinates of the point at an angle of $ frac{pi}{4} $ are:$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2} right) $ Answer 2 Matthew...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Explain the coordinates of a point on the unit circle at an angle of $ frac{pi}{4} $ Answer 1 Thomas Walker The unit circle is a circle with a radius of 1, centered at the origin (0, 0) in the coordinate plane. The coordinates of a point on the unit circle...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the exact values of $ an( heta) $ for $ heta = frac{5pi}{6} $, $ heta = frac{3pi}{4} $, and $ heta = frac{7pi}{4} $ from the unit circle. Answer 1 Olivia Lee To determine the exact values of $ tan(theta) $ for the given angles using the unit circle, we...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the quadrant in which an angle lies given its $sin$ and $cos$ values on the unit circle Answer 1 Isabella Walker Given that the sine and cosine values of an angle are both positive, the angle lies in the first quadrant. Answer 2 Joseph Robinson Given...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle where the angle $ heta $ equals $ frac{pi}{4} $ Answer 1 Maria Rodriguez To determine the coordinates of a point on the unit circle where $ theta $ equals $ frac{pi}{4} $, we use the unit circle equation:$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $ sec(θ) $ at $ θ = frac{pi}{3} $ on the unit circle Answer 1 Isabella Walker To find the value of $ sec(θ) $ at $ θ = frac{pi}{3} $ on the unit circle, we first find the cosine of the angle:$ cosleft(frac{pi}{3}right) = frac{1}{2} $Then, since...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Identify the coordinates of points on the unit circle for given angles $ heta $ Answer 1 Isabella Walker For the angle $ theta = frac{pi}{6} $, the point on the unit circle is given by $ (cos(frac{pi}{6}), sin(frac{pi}{6})) $. Calculate these values: $...