by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home What is the cosine and sine of the angle $frac{pi}{4}$ on the unit circle? Answer 1 Ava Martin To find the cosine and sine of the angle $frac{pi}{4}$ on the unit circle, we need to recall the coordinates of the point where the terminal side of the angle...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the cotangent of $ frac{pi}{4} $ on the unit circle. Answer 1 Maria Rodriguez To find the cotangent of $ frac{pi}{4} $ on the unit circle, we use the definition of cotangent in terms of sine and cosine. $ cot theta = frac{cos theta}{sin theta} $ For $ theta...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the value of $sec( heta)$ using the unit circle when $ heta = frac{2pi}{3}$, and verify the result using three different methods. Answer 1 Isabella Walker First, we find the coordinates of the point on the unit circle corresponding to $theta = frac{2pi}{3}$....
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Determine the cosine value at specific points on the unit circle. Answer 1 Michael Moore $text{Consider the point where the angle is } 60^circ text{ on the unit circle.}$ $text{The cosine of } 60^circ text{ is given by } cos(60^circ) = frac{1}{2}....
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the sine and cosine values for the angle $frac{5pi}{6}$ using the unit circle. Answer 1 Maria Rodriguez First, locate the angle $frac{5pi}{6}$ on the unit circle.The angle $frac{5pi}{6}$ is in the second quadrant.In the second quadrant, sine is positive and...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the value of $ an$ for given angles on the unit circle Answer 1 Daniel Carter Consider the angle $theta = frac{3pi}{4}$ on the unit circle.First, determine the reference angle. The reference angle for $frac{3pi}{4}$ is $frac{pi}{4}$.Since $frac{3pi}{4}$ is...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home $ ext{Cosine Values on the Unit Circle}$ Answer 1 Olivia Lee Consider the point $P(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle. Determine the cosine of the angle $theta$ corresponding to this point.Solution:On the unit circle, the coordinates of a point...
by zhanhongyuan | Feb 9, 2025 | Math
Home Find the equation of a circle passing through the point $(3, 4)$ and having its center at the point $(1, 2)$. Answer 1 Isabella Walker The general equation of a circle centered at $(h, k)$ with radius $r$ is: $ (x – h)^2 + (y – k)^2 = r^2 $ Here, the...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the slope of the tangent line to the unit circle at the point where $ heta = frac{pi}{4}$. Answer 1 Abigail Nelson To find the slope of the tangent line to the unit circle at the point where $theta = frac{pi}{4}$, we start by finding the coordinates of the...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the exact values of $sin$, $cos$, and $ an$ for the angle $225^{circ}$ using the unit circle. Answer 1 William King To find the exact values of $sin$, $cos$, and $tan$ for the angle $225^{circ}$ using the unit circle, we first note that $225^{circ}$ is in...