by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the cosine of $ frac{2pi}{3} $ radians on the unit circle Answer 1 Christopher Garcia The angle $ frac{2pi}{3} $ radians is in the second quadrant.In the second quadrant, the cosine of an angle is negative.For $ frac{2pi}{3} $ radians, the reference angle is...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Prove that the integral of $ exp(i heta) $ over a complete unit circle is zero. Answer 1 Christopher Garcia To prove that the integral of $ exp(i theta) $ over a complete unit circle is zero, we evaluate the contour integral: $ int_0^{2pi} exp(i theta) dtheta $...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the sine and cosine values for an angle of $ frac{π}{3} $ on the unit circle Answer 1 William King To find the sine and cosine values for an angle of $ frac{π}{3} $ on the unit circle, we need to recall the special angles on the unit circle. For $ frac{π}{3}...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home > Page 37 Do unit circles have diameter of $1$ Answer 1 Mia Harris A unit circle is defined as a circle with a radius of $1$ unit.The diameter of a circle is twice the radius.Therefore, for a unit circle:$ text{Diameter} = 2 times text{Radius} = 2 times 1 = 2...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the tangent values at $ 0 $, $ frac{pi}{4} $, and $ frac{pi}{2} $ on the unit circle Answer 1 Ella Lewis To find the tangent values at specific points on the unit circle, we use the definition of the tangent function, which is $ tan(theta) =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle is $ frac{pi}{4} $ radians Answer 1 Lucas Brown To find the coordinates of the point on the unit circle where the angle is $ frac{pi}{4} $ radians, we use the unit circle definition:The...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Identify the coordinates on the unit circle for angle $ heta $ Answer 1 Amelia Mitchell The coordinates of a point on the unit circle for a given angle $ theta $ are given by:$ ( cos(theta), sin(theta) ) $For example, if $ theta = frac{pi}{4} $:$ (...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home ”Find Answer 1 Ella Lewis To find the values of $ tan(theta) $ that satisfy the equation $ tan(theta) = 2 $ in the interval $ [0, 2pi] $, we need to determine the angles where the tangent function equals 2.First, recall that the tangent function is periodic...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Solve the equation to find all distinct points where the ellipse intersects the unit circle Answer 1 Michael Moore To find where the ellipse $frac{x^2}{a^2} + frac{y^2}{b^2} = 1$ intersects the unit circle $x^2 + y^2 = 1$, we need to solve the system of...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the sine and cosine values of $ frac{5pi}{6} $ Answer 1 John Anderson To determine the sine and cosine values of $ frac{5pi}{6} $, we refer to the unit circle.The angle $ frac{5pi}{6} $ is located in the second quadrant.In the second quadrant, sine is...