Find the coordinates on the unit circle at different angles

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Find the coordinates on the unit circle at different angles Answer 1 Isabella Walker To find the coordinates on the unit circle at 45 degrees:The unit circle equation is given by:$x^2 + y^2 = 1$For an angle of (45^{circ}) or (frac{pi}{4}) radians, the coordinates...

Find the angle θ in the unit circle where cos(θ) = -1/2

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Find the angle $ heta $ in the unit circle where $ cos( heta) = -frac{1}{2} $ Answer 1 Thomas Walker First, recall that cosine represents the x-coordinate on the unit circle. The cosine of $ theta $ equals $ -frac{1}{2} $ at the angles $ theta = frac{2pi}{3} $...

Given the unit circle, find all angles θ in the interval [0, 2π) such that sin(θ) = cos(θ), and prove your answer

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home ”Given Answer 1 Sophia Williams We start by setting the equation:$sin(theta) = cos(theta)$We know from trigonometric identities that:$sin(theta) = cos(theta)$Dividing both sides by $cos(theta)$ (assuming $cos(theta) neq 0$):$frac{sin(theta)}{cos(theta)} =...

Find the coordinates of a point on the unit circle that satisfies a given trigonometric equation

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home $ ext{Find the coordinates of a point on the unit circle that satisfies a given trigonometric equation.}$ Answer 1 Henry Green Let the point be $(x, y)$. Since it lies on the unit circle, we have $x^2 + y^2 = 1$. Consider the trigonometric equation $cos(2theta) +...

Find the sine, cosine, and tangent of the angle π/4 on the unit circle

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Find the sine, cosine, and tangent of the angle $frac{pi}{4}$ on the unit circle Answer 1 John Anderson First, let’s find the coordinates of the angle $frac{pi}{4}$ on the unit circle. The unit circle has a radius of 1, and the coordinates at an angle...

Given a unit circle centered at the origin, find the points where the circle intersects the line $y = 2x + 3$

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Given a unit circle centered at the origin, find the points where the circle intersects the line $y = 2x + 3$. Answer 1 Amelia Mitchell To find the points of intersection between the line $y = 2x + 3$ and the unit circle $x^2 + y^2 = 1$, we substitute $y = 2x +...

Given a point (a, b) on the unit circle, find the angle θ (in radians) between the line connecting the origin to the point and the positive x-axis

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Given a point $(a, b)$ on the unit circle, find the angle $ heta$ (in radians) between the line connecting the origin to the point and the positive x-axis. Answer 1 Abigail Nelson To find the angle $theta$ between the line connecting the origin to the point $(a,...

Find the sine and cosine values of the angle $\theta = \frac{\pi}{4}$ on the unit circle

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Find the sine and cosine values of the angle $ heta = frac{pi}{4}$ on the unit circle. Answer 1 Isabella Walker To find the sine and cosine values for $theta = frac{pi}{4}$, we refer to the unit circle. On the unit circle, the coordinates of the point...

Find the sine, cosine, and tangent values for the angle 45° on the unit circle

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home Find the sine, cosine, and tangent values for the angle 45° on the unit circle. Answer 1 Ava Martin To solve for the sine, cosine, and tangent values for the angle $45^{circ}$ on the unit circle, we use the following properties of the unit circle:The coordinates...

On the unit circle, find the coordinates of the point corresponding to the angle $\frac{5\pi}{4}$ radians

by zhanhongyuan | Feb 15, 2025 | Unit Circle

Home On the unit circle, find the coordinates of the point corresponding to the angle $frac{5pi}{4}$ radians. Answer 1 Joseph Robinson To find the coordinates of the point corresponding to the angle $frac{5pi}{4}$ radians on the unit circle, we utilize the unit...