by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Given a point on a unit circle with coordinates $(x, y)$ and angle $ heta$ from the positive $x$-axis, find the coordinates of the point after rotating by $45^circ$ counterclockwise. Answer 1 Maria Rodriguez Given the initial coordinates $(x, y)$ and angle...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home $In which quadrant does the angle lie on the unit circle?$ Answer 1 Mia Harris $Given an angle of 150^{circ}, we need to determine which quadrant it lies in.$ $Quadrant , I: 0^{circ} leq theta < 90^{circ}$ $Quadrant , II: 90^{circ} leq theta < 180^{circ}$...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Determine the coordinates on the unit circle for $150^circ$ and the corresponding angles in radians. Answer 1 Emily Hall First, convert $150^circ$ to radians: $theta = 150^circ times frac{pi}{180^circ} = frac{5pi}{6}$ Next, use the radian measure to find the...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Find the coordinates on the unit circle for an angle of $frac{pi}{4}$ Answer 1 Lily Perez To find the coordinates on the unit circle for an angle of $frac{pi}{4}$, we need to use the unit circle definition.The unit circle has a radius of 1, and the coordinates...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home In which quadrant does the angle $150^{circ}$ lie in the unit circle? Answer 1 Chloe Evans To determine the quadrant where the angle $150^{circ}$ lies, we divide the unit circle into four quadrants:1. Quadrant I: txt1 txt1 txt1^{circ}$ to $90^{circ}$2. Quadrant...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home $ ext{Find the coordinates of the point on the unit circle at } 45^{circ}$ Answer 1 Ava Martin To find the coordinates of a point on the unit circle at a given angle, we use the angle to find the cosine and sine values, which correspond to the x and y...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home $ ext{What is the sine of } 30^{circ} ext{ on the unit circle?}$ Answer 1 William King To find the sine of 30 degrees on the unit circle, we need to identify the coordinates of the point on the unit circle corresponding to this angle.In the unit circle, each...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home What are the sine and cosine values of $45^{circ}$ on the unit circle? Answer 1 Isabella Walker First, let’s convert 45 degrees into radians using the conversion factor $pi / 180$. $text{Radians} = 45 times frac{pi}{180} = frac{pi}{4}$ On the unit circle,...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Find the value of $sin( heta)$ for $ heta = frac{7pi}{6}$ using the unit circle. Answer 1 Joseph Robinson To find $sin(theta)$ for $theta = frac{7pi}{6}$, we need to locate the angle on the unit circle.First, note that $frac{7pi}{6}$ is in the third quadrant...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Determine Specific Coordinates on the Unit Circle Answer 1 Mia Harris Given a point on the unit circle defined by the angle $theta$ in radians, find the coordinates of the point where $theta = frac{5pi}{6}$.First, recall that any point on the unit circle is...