by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the integral of $ sec(x) $ along the unit circle Answer 1 Matthew Carter To evaluate the integral of $ sec(x) $ along the unit circle, we consider the parametrization of the unit circle. The unit circle can be parametrized as $ x = cos(theta) $ and $ y =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Prove that $ sin(frac{pi}{6}) $ using the unit circle Answer 1 Samuel Scott To prove that $ sin(frac{pi}{6}) $ using the unit circle, we start by locating the angle $ frac{pi}{6} $ on the unit circle.The angle $ frac{pi}{6} $ corresponds to 30 degrees.Using the...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the values of $cos( heta)$ and $sin( heta)$ using the unit circle when Define the unit circle in trigonometry ≤ heta ≤ 2pi$ and $ heta$ is a solution to the equation $ an( heta) = sqrt{3}$ Answer 1 Michael Moore The equation $tan(theta) = sqrt{3}$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of angle $ heta $ where $ cos( heta) = -frac{1}{2} $ on the unit circle Answer 1 Ella Lewis The cosine function represents the x-coordinate on the unit circle. Thus, finding $ cos(theta) = -frac{1}{2} $ involves finding the angles where the...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the angle in radians and degrees for the point $ left(-frac{1}{2}, -frac{sqrt{3}}{2} ight) $ on the unit circle Answer 1 Maria Rodriguez We need to find the angle corresponding to the point $ left(-frac{1}{2}, -frac{sqrt{3}}{2}right) $ on the unit circle....
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $ arcsin(frac{1}{2}) $ in radians using the unit circle. Answer 1 William King To find the value of $ arcsin(frac{1}{2}) $, consider the unit circle and the definition of arcsin. The arcsin function outputs the angle whose sine is the given...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $cosleft(frac{3pi}{4} ight)$. Answer 1 Alex Thompson The unit circle helps us locate the angle $theta = frac{3pi}{4}$ which lies in the second quadrant. The reference angle for $theta = frac{3pi}{4}$ is: $pi – frac{3pi}{4} = frac{pi}{4}$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle Answer 1 Benjamin Clark To find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle, we use the unit circle definition. The unit...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home How to find the reference angle for any angle not on the unit circle Answer 1 Charlotte Davis To find the reference angle for an angle θ not on the unit circle, you must first locate the angle in the appropriate quadrant. The reference angle is then the smallest...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Given that $ cos(θ) = -frac{1}{2} $, find the general solutions for $ θ $ in the unit circle. Answer 1 Emma Johnson To solve for $ θ $ such that $ cos(θ) = -frac{1}{2} $, we need to find all angles in the unit circle where the cosine value is $ -frac{1}{2} $. The...