by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Techniques to Remember the Unit Circle for High School Students Answer 1 Amelia Mitchell One way to remember the unit circle is by focusing on the key angles and their coordinates. Let’s start with the four quadrants: $0, frac{pi}{2}, pi, frac{3pi}{2}, 2pi$...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home What is the value of $ an(45°)$ on the unit circle? Answer 1 Henry Green To find the value of $tan(45°)$ on the unit circle, we use the definition of tangent:$tan(theta) = frac{sin(theta)}{cos(theta)}$At $theta = 45°$, we have:$sin(45°) =...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home ”Find Answer 1 Thomas Walker To solve the problem, we need to find all angles $theta$ such that $tan(theta) = 3$ within the interval $[0, 2pi]$.Step 1: Recognize that $tan(theta)$ is positive in the first and third quadrants.Step 2: The reference angle...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the values of $sin(30°)$ and $cos(30°)$ on the unit circle. Answer 1 Joseph Robinson To find the values of $sin(30°)$ and $cos(30°)$ on the unit circle, we use the fact that 30° corresponds to $frac{pi}{6}$ radians.The coordinates of the point on the unit...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home What is the value of $cot(45^circ)$ on the unit circle? Answer 1 Benjamin Clark To find the cotangent of 45 degrees, we use the definition of cotangent on the unit circle:$cot(theta) = frac{cos(theta)}{sin(theta)}$For $theta = 45^circ$, we know that:$cos(45^circ)...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the sine and cosine values for the angle $frac{5pi}{6}$ Answer 1 Chloe Evans To find the sine and cosine values for the angle $frac{5pi}{6}$, we first understand that this angle is located in the second quadrant of the unit circle. The reference angle for...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the angles on the unit circle where the cosine value is equal to $-frac{1}{2}$. Answer 1 Christopher Garcia To find the angles on the unit circle where the cosine value is equal to $-frac{1}{2}$, we start by considering the unit circle properties and the...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Determine the coordinates of the point where the terminal side of an angle $ heta = frac{5pi}{4}$ radians intersects the unit circle. Answer 1 Mia Harris To find the coordinates of the point where the terminal side of an angle $theta = frac{5pi}{4}$ intersects...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the value of $cos( heta)$ and $sin( heta)$ for $ heta = 225^circ$ Answer 1 Lucas Brown First, we need to find the reference angle for $theta = 225^circ$. Since $225^circ$ is in the third quadrant, the reference angle is:$225^circ – 180^circ =...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the value of $cos(-pi / 3)$ using the unit circle. Answer 1 Henry Green To find $cos(-pi / 3)$, we can start by recognizing that the cosine function is even. This means $cos(-x) = cos(x)$. Therefore:$cos(-pi / 3) = cos(pi / 3)$From the unit circle, we know...