by zhanhongyuan | Feb 9, 2025 | Math
Home $Finding;the;Tangent;to;a;Unit;Circle$ Answer 1 Daniel Carter The problem is to find the equation of the tangent to a unit circle at a given point.Given a unit circle with the equation:$x^2 + y^2 = 1$and a point ((a, b)) on the circle. Since ((a, b)) is on the...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home ”Given Answer 1 Lily Perez Given the point on the unit circle $left( -frac{3}{5}, -frac{4}{5} right)$, we need to determine the angle $theta$ in radians.First, note that the x and y coordinates tell us which quadrant the angle is in. Both coordinates are...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Given a point P on the unit circle at an angle $ heta $ (in radians) from the positive x-axis, find the coordinates of P if $ heta $ is transformed by the function $ f( heta) = 2 heta + frac{pi}{4} $. Also, identify the new x and y coordinates aft Answer 1 Ella...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Finding the Coordinates of a Point on the Unit Circle Answer 1 Thomas Walker Given an angle of $theta = frac{pi}{3}$ radians, find the coordinates of the corresponding point on the unit circle.First, recall the unit circle definition: for any angle $theta$, the...
by zhanhongyuan | Feb 9, 2025 | Math
Home Find the circumference of a circle with a radius of 7 units. Answer 1 Olivia Lee First, we use the formula for the circumference of a circle:$C = 2 pi r$Substituting the radius (r) given in the problem:$C = 2 pi times 7$Simplify the expression:$C = 14pi$The...
by zhanhongyuan | Feb 9, 2025 | Math
Home $Finding the Tangent Line to a Unit Circle at a Given Point$ Answer 1 Daniel Carter Consider the unit circle centered at the origin with the equation: $x^2 + y^2 = 1.$ To find the equation of the tangent line to the circle at a given point $P(a, b)$ on the...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Find the sine and cosine values for the angle $ heta = 45^{circ}$ on the unit circle. Answer 1 Mia Harris To find the sine and cosine values for the angle $theta = 45^{circ}$ on the unit circle:1. Note that $theta = 45^{circ}$ is in the first quadrant.2. The...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Given that $ csc( heta) = 2 $ and $ heta $ lies in the second quadrant, find the exact value of $ heta $ and verify using trigonometric identities. Answer 1 John Anderson Given: $ csc(theta) = 2 $ Since ( csc(theta) = frac{1}{sin(theta)} ), we get: $ sin(theta) =...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home What are the coordinates of the point on the unit circle corresponding to an angle of $45^circ$? Answer 1 John Anderson To determine the coordinates of the point on the unit circle at $45^circ$, we use the fact that the unit circle has a radius of 1 and the...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home $ ext{Determine the coordinates of a point on a unit circle with a given angle}$ Answer 1 Ella Lewis Let’s find the coordinates of a point on the unit circle corresponding to an angle of $frac{5pi}{4}$ radians.The unit circle equation is given by:$x^2 + y^2...