by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ arctan(sin(frac{3pi}{4})) $ Answer 1 Emma Johnson To find the value of $ arctan(sin(frac{3pi}{4})) $, we first need to find the value of $ sin(frac{3pi}{4}) $.$ sin(frac{3pi}{4}) = sin(pi – frac{pi}{4}) = sin(frac{pi}{4}) =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle with the positive $x$-axis is $frac{pi}{3}$ Answer 1 Amelia Mitchell The unit circle is defined as a circle with radius 1 centered at the origin. The coordinates of any point on the unit circle...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point where the terminal side of an angle $ heta$ intersects the unit circle, given that $ heta = frac{5pi}{6}$ Answer 1 Sophia Williams To determine the coordinates where the terminal side of $theta = frac{5pi}{6}$ intersects the unit...
by zhanhongyuan | Feb 3, 2025 | Math
Home Calculate the area of a sector of a circle with radius $ r $ and central angle $ heta $ (in radians) Answer 1 Maria Rodriguez The area of a sector of a circle with radius $ r $ and central angle $ theta $ can be calculated using the formula:$ A = frac{1}{2} r^2...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the exact values of $sin(frac{5pi}{6})$ and $cos(frac{5pi}{6})$ in the unit circle Answer 1 Samuel Scott To determine the exact values of $sin(frac{5pi}{6})$ and $cos(frac{5pi}{6})$, we use the unit circle.For the angle $frac{5pi}{6}$, it is in the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Given a point on the unit circle, find the corresponding angle $ heta $ and verify the coordinates Answer 1 Matthew Carter Let Answer 2 Alex Thompson Consider the point $(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle. This corresponds to the angle $ heta $...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the value of $ an( heta) $ at $ heta = frac{3pi}{4} $ using the unit circle chart. Answer 1 James Taylor To determine the value of $ tan(theta) $ at $ theta = frac{3pi}{4} $, we use the unit circle chart. The angle $ frac{3pi}{4} $ is in the second...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle at angle $ frac{pi}{3} $ Answer 1 Amelia Mitchell The unit circle has a radius of 1. The coordinates of a point on the circle at angle $ frac{pi}{3} $ are given by:$ (cos(frac{pi}{3}), sin(frac{pi}{3}))...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ for $ heta $ in the second quadrant of the unit circle Answer 1 Emily Hall In the second quadrant, the angle $ theta $ ranges from $ frac{pi}{2} $ to $ pi $. Here, $ sin(theta) $ is...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ sinleft(frac{pi}{3} ight) $ on the unit circle Answer 1 Benjamin Clark To find the value of $ sinleft(frac{pi}{3}right) $ on the unit circle, we look at the reference angle for $ frac{pi}{3} $.The reference angle is $ 60^{circ} $, and the sine...