by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Find the sine and cosine values for an angle of $frac{5pi}{4}$ radians on the unit circle. Answer 1 Ava Martin To find the sine and cosine values for an angle of $frac{5pi}{4}$ radians, we need to locate this angle on the unit circle.First, we recognize that...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Determine the Quadrant of Multiple Angles on the Unit Circle Answer 1 Daniel Carter Given the angles $30^circ$, $150^circ$, and $240^circ$, determine the quadrant each angle lies in on the unit circle. 1. For $30^circ$, it is in the first quadrant because it is...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle given a specific angle. Answer 1 James Taylor Given an angle ( theta = frac{5pi}{6} ), find the coordinates of the corresponding point on the unit circle.1. The angle ( frac{5pi}{6} ) is in the second...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Find the tangent of angle $frac{pi}{3}$ using the unit circle. Answer 1 John Anderson To find the tangent of angle $frac{pi}{3}$ using the unit circle, we need to find the coordinates of the point where the terminal side of the angle intersects the unit...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Determine the quadrant of point P on the unit circle where $P$ has coordinates $(cos( heta), sin( heta))$, given that $ heta = 210$ degrees. Answer 1 Olivia Lee First, convert the given angle to radians:$theta = 210^circ times frac{pi}{180^circ} =...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Given the point $P(a, b)$ on the unit circle, find the exact values of sine, cosine, and tangent for the angles $ heta$ and $phi$ where $ heta$ is the angle between the positive x-axis and the line segment $OP$ and $phi$ is the angle in radians corres Answer 1...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Convert $frac{5pi}{6}$ radians to degrees and find the sine and cosine values on the unit circle. Answer 1 Alex Thompson First, we convert radians to degrees: $text{Degrees} = frac{5pi}{6} times frac{180}{pi} = frac{5 times 180}{6} = 150^{circ}$ Next, we identify...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home $ ext{Easy Ways to Remember the Unit Circle}$ Answer 1 Ava Martin One of the easiest ways to remember the unit circle is by understanding the key angles and their coordinates. The unit circle has a radius of 1, and key angles are 0°, 30°, 45°, 60°, 90°, etc....
by zhanhongyuan | Feb 13, 2025 | Math
Home Find the circumference and area of a circle with a radius of $5 ext{ cm}$. Answer 1 Charlotte Davis To find the circumference of a circle, we use the formula: $C = 2pi r$ Plugging in the radius of 5 cm: $C = 2 pi (5) = 10 pi approx 31.42 text{ cm}$ To find the...
by zhanhongyuan | Feb 13, 2025 | Unit Circle
Home Solve for the exact values of sine and cosine for the angle $frac{7pi}{6}$ on the unit circle. Answer 1 Thomas Walker First, note that $frac{7pi}{6}$ radians is in the third quadrant where both sine and cosine are negative. The reference angle for $frac{7pi}{6}$...