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...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the area of a sector of a unit circle with a central angle of $ heta $ radians Answer 1 Chloe Evans To find the area of a sector of a unit circle with a central angle of $ theta $, we use the formula for the area of a sector:n$ A = frac{1}{2} r^2 theta...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ sin(frac{pi}{6}) $, $ cos(frac{pi}{3}) $, and $ an(frac{pi}{4}) $ using the unit circle chart Answer 1 Michael Moore Using the unit circle chart, we find:$ sinleft(frac{pi}{6}right) = frac{1}{2} $$ cosleft(frac{pi}{3}right) = frac{1}{2} $$...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ cos(frac{pi}{4}) $ and $ sin(frac{pi}{4}) $ using the unit circle Answer 1 Amelia Mitchell To find the values of $ cos(frac{pi}{4}) $ and $ sin(frac{pi}{4}) $ using the unit circle, we need to identify the coordinate point on the unit circle...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the equation of the tangent line to the unit circle at $(1, 0)$ Answer 1 Maria Rodriguez The unit circle is given by the equation:$ x^2 + y^2 = 1 $To find the equation of the tangent line at $(1, 0)$, we first find the slope of the tangent. Differentiate the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home What does the $ sin $ function represent on the unit circle? Answer 1 Chloe Evans On the unit circle, the sine function $ sin(theta) $ represents the y-coordinate of a point on the circle corresponding to the angle $ theta $ measured from the positive...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the values of trigonometric functions for specific angles on the unit circle Answer 1 Sophia Williams Given the angle $ theta = frac{5pi}{4} $ radians, find the values of $ sin(theta) $, $ cos(theta) $, and $ tan(theta) $. The coordinates of $...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ arcsin(frac{1}{2}) $ using the unit circle. Answer 1 Isabella Walker To find the value of $ arcsin(frac{1}{2}) $ using the unit circle, we need to determine the angle whose sine is $ frac{1}{2} $.On the unit circle, the sine of an angle is the...