by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the cosine of the angle at $ frac{3π}{4} $ radians on the unit circle Answer 1 Sophia Williams The unit circle helps us find the cosine of an angle. For an angle of $ frac{3π}{4} $ radians:The reference angle is $ x0crac{π}{4} $, and in the second quadrant,...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Prove that the equation $ x^2 + y^2 = 1 $ is satisfied by the coordinates of any point on the unit circle for a given angle $ heta $. Answer 1 William King To prove that the equation $ x^2 + y^2 = 1 $ is satisfied by the coordinates of any point on the unit...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the $ csc( heta) $ of an angle $ heta $ in the unit circle when its $ sin( heta) $ is equal to a rational value Answer 1 Abigail Nelson To evaluate $ csc(theta) $ when $ sin(theta) $ is a rational value, let Answer 2 Joseph Robinson To evaluate $ csc(...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle given the angle $ heta $ Answer 1 Thomas Walker To find the coordinates of a point on the unit circle given an angle $ theta $, we use the formulas for sine and cosine:n $ x = cos(theta) $n $ y = sin(theta) $n...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the coordinates of ( frac{3pi}{4} ) on the unit circle Answer 1 Joseph Robinson The angle ( frac{3pi}{4} ) is in the second quadrant of the unit circle. To find its coordinates, we start by noting that the reference angle for ( frac{3pi}{4} ) is (...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Calculate the length of the arc intercepted by a central angle $ heta $ on a unit circle Answer 1 Olivia Lee To calculate the length of the arc intercepted by a central angle $ theta $ on a unit circle, you can use the formula: $ s = r theta $ Since the radius $...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the angles on the unit circle Answer 1 Emma Johnson Given a point on the unit circle at coordinates (1/2, √3/2), find the corresponding angle in degrees.The point (1/2, √3/2) corresponds to an angle of 60 degrees. Answer 2 James Taylor Given a point on the...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the angle $ heta $ in radians for a point on the unit circle that satisfies given conditions Answer 1 Lily Perez Given a point $ P $ on the unit circle, where the coordinates of $ P $ are $ ( cos(theta), sin(theta) ) $.If the coordinates of $ P $ are given...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $sin(θ)$, $cos(θ)$, and $ an(θ)$ for $θ = fracπ3$ on the unit circle Answer 1 Charlotte Davis When $θ = fracπ3$, we can find the values of $sin(θ)$, $cos(θ)$, and $tan(θ)$ from the unit circle:$sin(fracπ3) = frac{sqrt3}2$$cos(fracπ3) =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the integral of $ cos(2x) $ from $ 0 $ to $ frac{pi}{2} $ Answer 1 Charlotte Davis To evaluate the integral of $ cos(2x) $ from $ 0 $ to $ frac{pi}{2} $:$ int_0^{frac{pi}{2}} cos(2x) , dx $Use the substitution $ u = 2x $, then $ du = 2dx $ or $ dx =...