by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the exact values of sine and cosine for the angle $ frac{pi}{4} $ using the unit circle Answer 1 Matthew Carter To find the exact values of sine and cosine for the angle $ frac{pi}{4} $, we use the unit circle.For $ theta = frac{pi}{4} $, the...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Identify the coordinates of specific angles on the unit circle. Answer 1 Olivia Lee To find the coordinates of specific angles on the unit circle, remember that the unit circle has a radius of 1.For the angle $theta = frac{pi}{4}$, the coordinates...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the area of a sector in a unit circle with a central angle of $ heta $ radians Answer 1 Joseph Robinson The formula to find the area of a sector in a unit circle is:$ A = frac{1}{2} theta $where $ theta $ is the central angle in radians.For example, if $...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the image of the unit circle under the transformation $ f(z)=z^2 $ Answer 1 Emily Hall The unit circle in the complex plane is given by $ |z| = 1 $, meaning any point $ z $ on the unit circle can be written as $ z = e^{itheta} $ for some real number $ theta...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Identify the quadrant in which the angle $ heta $ lies Answer 1 Samuel Scott To identify the quadrant in which the angle $ theta $ lies, follow these steps: 1. If $ 0 leq theta < frac{pi}{2} $, then the angle is in the first quadrant. 2. If $ frac{pi}{2} leq...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the value of $ cosleft( frac{pi}{3} ight) $ Answer 1 Maria Rodriguez The value of $ cosleft( frac{pi}{3} right) $ can be found using the unit circle. The angle $ frac{pi}{3} $ corresponds to 60 degrees. On the unit circle, the coordinates for the angle 60...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle at angle $frac{pi}{4}$ Answer 1 Lily Perez To find the coordinates of a point on the unit circle at angle $frac{pi}{4}$, we use the trigonometric functions:$ x = cosleft(frac{pi}{4}right) $$ y =...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the values of $ sin frac{5pi}{6} $, $ cos frac{5pi}{6} $, and $ an frac{5pi}{6} $ using the unit circle. Answer 1 Christopher Garcia To find the values of $ sin frac{5pi}{6} $, $ cos frac{5pi}{6} $, and $ tan frac{5pi}{6} $ using the unit circle, we first...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the points where the line $ y = mx + b $ is tangent to the unit circle Answer 1 Charlotte Davis To find the points where the line $ y = mx + b $ is tangent to the unit circle, we start with the equation of the unit circle:$ x^2 + y^2 = 1 $Substitute $ y = mx...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the value of $ an( heta) $ when $ heta $ is at the angle $ frac{pi}{4} $ on the unit circle Answer 1 James Taylor To find the value of $ tan(theta) $ when $ theta $ is at the angle $ frac{pi}{4} $ on the unit circle, we use the definition of tangent in terms...