Determine the coordinates of the point where the angle θ = π/3 on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the coordinates of the point where the angle $ heta = frac{pi}{3} $ on the unit circle Answer 1 Michael Moore First, recall that the unit circle has a radius of 1. For the angle $ theta = frac{pi}{3} $, we use the definitions of sine and cosine: $ x =...

Find the values of sin(θ) and cos(θ) where θ is 5π/4 radians on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the values of $sin( heta)$ and $cos( heta)$ where $ heta$ is $frac{5pi}{4}$ radians on the unit circle Answer 1 Maria Rodriguez Given $theta = frac{5pi}{4}$, we need to find the values of $sin(theta)$ and $cos(theta)$ on the unit circle.The angle...

Compute the integral of cos^2(t) on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Compute the integral of $ cos^2(t) $ on the unit circle Answer 1 Chloe Evans To compute the integral of $cos^2(t)$ on the unit circle, we can use the double-angle identity for cosine:$cos^2(t) = frac{1 + cos(2t)}{2}$Now, integrate:$int_0^{2pi} cos^2(t) , dt =...

Find the coordinates of the point on the unit circle where the angle is 5π/6

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle where the angle is $frac{5pi}{6}$. Answer 1 Ella Lewis To find the coordinates of the point on the unit circle where the angle is $frac{5pi}{6}$, we use the unit circle trigonometric identities for sine and...

Find the coordinates on the unit circle for an angle of pi/3

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the coordinates on the unit circle for an angle of $ frac{pi}{3} $ Answer 1 Joseph Robinson To find the coordinates on the unit circle for an angle of $ frac{pi}{3} $, we use the cosine and sine functions:$ x = cos(frac{pi}{3}) $$ y = sin(frac{pi}{3}) $The...

Find the coordinates of the point on the unit circle for an angle of 3π/4 radians

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle for an angle of $ frac{3pi}{4} $ radians Answer 1 James Taylor To find the coordinates of the point on the unit circle for an angle of $ frac{3pi}{4} $ radians, we need to use the unit circle definition:For an...

Determine the value of cos(π/4) using the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the value of $cos(frac{pi}{4})$ using the unit circle Answer 1 Chloe Evans To determine the value of $cos(frac{pi}{4})$, we use the unit circle. At the angle $frac{pi}{4}$, the coordinates on the unit circle are $(frac{sqrt{2}}{2},...

Find the values of sin(π/3), cos(π/3), and tan(π/3)

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the values of $sin(frac{pi}{3})$, $cos(frac{pi}{3})$, and $ an(frac{pi}{3})$ Answer 1 Benjamin Clark To find the values of $sin(frac{pi}{3})$, $cos(frac{pi}{3})$, and $tan(frac{pi}{3})$, we use the unit circle. For $theta = frac{pi}{3}$: $ sin(frac{pi}{3}) =...

Calculate the integral of 1/(1 + x^2) over the unit circle

by zhanhongyuan | Feb 4, 2025 | Math

Home Calculate the integral of $ frac{1}{1 + x^2} $ over the unit circle Answer 1 Benjamin Clark To calculate the integral of $ frac{1}{1 + x^2} $ over the unit circle, we first convert to polar coordinates: $ x = r cos(theta), y = r sin(theta) $ In polar coordinates,...

Determine the cosine and sine values at π/4 on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the cosine and sine values at $ frac{pi}{4} $ on the unit circle Answer 1 Lily Perez To find the cosine and sine values at $ frac{pi}{4} $ on the unit circle:$ cos left( frac{pi}{4} right) = frac{sqrt{2}}{2} $ $ sin left( frac{pi}{4} right) =...