by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the sine and cosine of the angle $ heta$ when $ heta = frac{pi}{6}$. Answer 1 Christopher Garcia To find the sine and cosine of the angle $theta$ when $theta = frac{pi}{6}$, we can use the unit circle.The angle $frac{pi}{6}$ radians corresponds to 30...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Given a unit circle centered at the origin, but flipped in a non-standard way such that the positive x-axis points downwards and the positive y-axis points to the left, find the coordinates of the point corresponding to an angle of $frac{5pi}{6}$ radian Answer 1...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the value of $cos( heta)$ on the unit circle for a given $ heta$ and determine the exact coordinates of the corresponding point. Answer 1 Chloe Evans Let’s consider the angle $ theta = frac{7pi}{6}$. First, we determine the reference angle. Since...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle with the positive x-axis is $frac{5pi}{6}$ radians. Answer 1 Daniel Carter Given the angle $theta = frac{5pi}{6}$ radians, we need to find the coordinates of the point on the unit circle.On the...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the coordinates of the point where the line $y = 2x$ intersects the unit circle. Answer 1 Abigail Nelson First, let’s write the equation of the unit circle: $x^2 + y^2 = 1.$ Since $y = 2x$, we can substitute $2x$ for $y$ in the unit circle equation:...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the sine, cosine, and tangent of an angle of $45^circ$ on the unit circle. Answer 1 Charlotte Davis To find the sine, cosine, and tangent of an angle of 45 degrees on the unit circle:The coordinates of the point at $45^circ$ on the unit circle are...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Given the unit circle, find the coordinates of the point where the angle $ heta$ intersects the unit circle. Let $ heta = 45^circ$. Answer 1 Emma Johnson To find the coordinates of the point where the angle $theta = 45^circ$ intersects the unit circle, we use the...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home $ ext{Determine the Quadrants of Trigonometric Values on the Unit Circle}$ Answer 1 Matthew Carter To determine the quadrant of the angle $frac{5pi}{3}$ on the unit circle: 1. Identify the reference angle: $frac{5pi}{3} – 2pi = frac{-pi}{3}$, which is equal...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home $ ext{Find the cosine values of the angles on the unit circle}$ Answer 1 Chloe Evans Given the angle $theta = frac{5pi}{3}$, we need to find the cosine value. The unit circle coordinates at an angle $theta$ are given by $(cos(theta), sin(theta))$. For $theta =...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the points of intersection between the unit circle and the line $y = 2x + 1$ Answer 1 Ava Martin To find the points of intersection, we can substitute $y = 2x + 1$ into the equation of the unit circle, which is $x^2 + y^2 = 1$.$x^2 + (2x + 1)^2 = 1$Expanding...