by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the coordinates on the unit circle at an angle of $ frac{pi}{3} $ Answer 1 Christopher Garcia To find the coordinates on the unit circle at an angle of $ frac{pi}{3} $, we use the unit circle definition: $ (cos(theta), sin(theta)) $For $ theta = frac{pi}{3}...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the values of $ heta $ that satisfy both $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $ Answer 1 Ava Martin First, recognize that $ sin(theta) = -frac{1}{2} $ in the third and fourth quadrants. The angles in these quadrants are $...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the hypotenuse of a right triangle on the unit circle with one side equal to $ frac{1}{sqrt{2}} $ Answer 1 Amelia Mitchell In a right triangle on the unit circle, the hypotenuse is always 1. If one side is $ frac{1}{sqrt{2}} $, the other side must also be $...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the value of $sin$, $cos$, and $ an$ for the angle $ heta = frac{pi}{4}$ using the unit circle Answer 1 Daniel Carter Given the angle $theta = frac{pi}{4}$, the corresponding coordinates on the unit circle are:$ (cos(theta), sin(theta)) =...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians. Answer 1 Emma Johnson To find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians, we use the unit circle definition:The...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the exact values of the trigonometric functions for angle $ frac{7pi}{6} $ Answer 1 Olivia Lee To determine the exact values of the trigonometric functions for angle $ frac{7pi}{6} $, we follow these steps:1. Recognize that $ frac{7pi}{6} $ is in the...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle where the angle is given by $ heta = frac{3}{4} pi $ Answer 1 William King The unit circle Answer 2 Sophia Williams The coordinates of the point for $ heta = frac{3}{4} pi $ are found using:$ x =...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Identify the quadrant of the unit circle where the angle $ heta = frac{3pi}{4} $ lies Answer 1 Christopher Garcia To identify the quadrant where the angle $ theta = frac{3pi}{4} $ lies, we need to examine the unit circle.$ frac{3pi}{4} $ is in radians.The angle $...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Determine the quadrant of various points on the unit circle Answer 1 Alex Thompson To determine the quadrant of a point on the unit circle, consider the signs of the x and y coordinates:Quadrant I: Both coordinates are positive ($x > 0$, $y > 0$)Quadrant II: x is...
by zhanhongyuan | Feb 5, 2025 | Unit Circle
Home Calculate $ cos(frac{pi}{4}) $ using the unit circle Answer 1 Sophia Williams To calculate $ cos(frac{pi}{4}) $ using the unit circle, we look at the angle $ frac{pi}{4} $ on the unit circle.At this angle, both sine and cosine values are equal.Thus, the value of...