by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the coordinates of a point in the first quadrant of the unit circle given its angle $ heta $ Answer 1 Daniel Carter To determine the coordinates of a point in the first quadrant on the unit circle given its angle $ theta $, we use the trigonometric...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the exact value of the inverse trig function expressions Answer 1 Maria Rodriguez Consider the expression $ sin^{-1}left( frac{sqrt{3}}{2} right) $. We know that $ sinleft( frac{pi}{3} right) = frac{sqrt{3}}{2} $. Therefore, $ sin^{-1}left( frac{sqrt{3}}{2}...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the points where the ellipse intersects the empty unit circle Answer 1 Lucas Brown To find the points where the ellipse intersects the empty unit circle, we start with the equations of the ellipse and the empty unit circle:Ellipse: $x0crac{x^2}{a^2} +...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the points of intersection between the unit circle and the curve $ y = x^3 - x $ Answer 1 Christopher Garcia To find the points of intersection between the unit circle $x^2 + y^2 = 1$ and the curve $y = x^3 – x$, we substitute $y$ from the second...
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)...