by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle at angle $ heta = frac{pi}{4} $ Answer 1 Joseph Robinson The coordinates of the point on the unit circle at angle $ theta = frac{pi}{4} $ can be found using the sine and cosine functions: The x-coordinate is: $...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home How to remember the unit circle using trigonometric identities Answer 1 Daniel Carter To remember the unit circle, you can leverage trigonometric identities and properties:1. Know the key angles and their corresponding coordinates: txt1 txt1 txt1, frac{pi}{6},...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the sine and cosine of $ frac{pi}{4} $ Answer 1 Michael Moore To find the sine and cosine of $ frac{pi}{4} $, we use the unit circle. Since $ frac{pi}{4} $ corresponds to 45 degrees:$ sinleft( frac{pi}{4} right) = frac{sqrt{2}}{2} $$ cosleft( frac{pi}{4}...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Prove the identity of $ sin( heta) $ on the unit circle. Answer 1 Isabella Walker To prove the identity of $ sin(theta) $ on the unit circle, we start by considering a point on the unit circle at angle $ theta $. The coordinates of this point can be represented...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home How to calculate points on the unit circle for specific angles Answer 1 Christopher Garcia To calculate points on the unit circle for a specific angle $ theta $, follow these steps: 1. Recall that the unit circle is a circle with radius 1 centered at the origin...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Given that $ an( heta) = 2 $ and $ heta $ is in the second quadrant, find the exact values of $ sin( heta) $ and $ cos( heta) $. Answer 1 Chloe Evans 1. Given that $ tan(theta) = 2 $, we can write:$ tan(theta) = frac{sin(theta)}{cos(theta)} = 2 $Let $ sin(theta)...
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...