by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the angle $ heta $ on the unit circle where the following conditions are met: $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $ Answer 1 Charlotte Davis To find the angle $ theta $ on the unit circle where $ sin(theta) = -frac{1}{2} $ and $...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $csc(θ)$ when $θ = frac{π}{6}$ on the unit circle Answer 1 Olivia Lee To find the value of $csc(θ)$ when $θ = frac{π}{6}$ on the unit circle, we first find the sine of $θ$:$ sin(frac{π}{6}) = frac{1}{2} $Since $csc(θ) = frac{1}{sin(θ)}$, we...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the exact value of $ cos(frac{pi}{9}) $ using the unit circle and trigonometric identities Answer 1 Ava Martin To find the exact value of $ cos(frac{pi}{9}) $, we can use the triple-angle identity for cosine:n$ cos(3theta) = 4cos^3(theta) – 3cos(theta)...
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: $pi – frac{3pi}{4} = frac{pi}{4}$...