by zhanhongyuan | Feb 11, 2025 | Ai Tools
DeepSeek’s Current Landscape Since launching its advanced R1 model in January 2025, DeepSeek has rapidly partnered with global tech giants and open-source communities to democratize AI accessibility. The R1 model is renowned for its cost efficiency, mathematical...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the exact values of the $cos$ and $sin$ for three points on the unit circle. Answer 1 Henry Green Given points on the unit circle: $frac{pi}{6}, frac{5pi}{4}, frac{11pi}{6}$, find the exact values of $cos$ and $sin$. Answer 2 Daniel Carter For $ heta =...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home $ ext{Prove the relationship between the sine and cosine of the sum of two angles using the unit circle.}$ Answer 1 Samuel Scott To prove the relationship between the sine and cosine of the sum of two angles, we use the unit circle and the definitions of sine and...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the Coordinate on the Unit Circle Answer 1 Mia Harris Given the angle $theta = frac{pi}{4}$, find the coordinate on the unit circle.The angle $theta = frac{pi}{4}$ is equivalent to 45 degrees. At this angle, both the x and y coordinates are equal. Since we...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the cosine and sine of an angle on the unit circle at $frac{5pi}{6}$ radians. Answer 1 Abigail Nelson To find the cosine and sine values for $frac{5pi}{6}$ radians, first recognize that $frac{5pi}{6}$ is in the second quadrant of the unit circle.In the...
by hanjianwei | Feb 11, 2025 | Ai Tools
PopAi: Leading AI for George Washington Image Generation So, if you’ve never tried out PopAi’s AI Image generator, you’re seriously missing out. I remember the first time I played around with it—man, was I impressed! After experimenting with PopAi, I was blown away by...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Given a point on the unit circle in Cartesian coordinates, find its other coordinate and the angle it makes with the positive x-axis. Answer 1 James Taylor To solve this problem, we start by using the unit circle equation: $x^2 + y^2 = 1$ Given a point (x, y) =...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Calculate the sine and cosine values for $225^{circ}$ using the unit circle. Answer 1 Thomas Walker The unit circle helps us determine the sine and cosine values for any given angle. For the angle $225^{circ}$, we need to find its location on the unit circle.The...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home On the unit circle, find the value of $cos(135°) + sin(225°) + an(315°)$. Answer 1 Thomas Walker $ cos(135°) $ Since $135°$ lies in the second quadrant, we have: $ cos(135°) = -cos(180° – 135°) = -cos(45°) = -frac{sqrt{2}}{2} $ $ sin(225°) $ Since $225°$...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home If the standard unit circle is flipped over the x-axis, describe the transformation of the angle $ heta$ and calculate the new coordinates for $ heta = frac{2pi}{3}$. Answer 1 Emily Hall When the unit circle is flipped over the x-axis, the y-coordinates of all...
