Given a circle with center O, radius r, and a point P outside the circle such that OP = d, find the length of the tangent segment from P to the circle

by zhanhongyuan | Feb 13, 2025 | Math

Home Given a circle with center O, radius $r$, and a point $P$ outside the circle such that $OP = d$, find the length of the tangent segment from $P$ to the circle. Answer 1 Emily Hall Let the tangent point be T. In the right triangle OTP, OT is the radius (r), and OP...

Find the value of \( \theta \) if \( \tan(\theta) = 2 \) and \( \theta \) is in the second quadrant Then, calculate the coordinates of the corresponding point on the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home $ ext{Find the value of } heta ext{ if } an( heta) = 2 ext{ and } heta ext{ is in the second quadrant. Then, calculate the coordinates of the corresponding point on the unit circle.} $ Answer 1 Matthew Carter We know that ( tan(theta) =...

Given a point P on the unit circle, find the coordinates of P if the angle formed with the positive x-axis is θ, where θ satisfies 0 ≤ θ ≤ 2π and the coordinates satisfy the equation of the circle x^2 + y^2 = 1 Provide three different coordinate sets for

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Given a point $P$ on the unit circle, find the coordinates of $P$ if the angle formed with the positive x-axis is $ heta$, where $ heta$ satisfies Define the unit circle in trigonometry leq heta leq 2pi$ and the coordinates satisfy the equation of the circle $x^2...

Find the sine of the angle located at 45 degrees on the unit circle

by zhanhongyuan | Feb 13, 2025 | Math

Home Find the sine of the angle located at (45^circ) on the unit circle. Answer 1 Maria Rodriguez For an angle of 45 degrees (or (frac{pi}{4}) radians) on the unit circle, we need to find the sine value. On the unit circle, the coordinates for an angle (theta) are...

Find the general solution for \( \theta \) in the equation \( \sin(\theta) = \frac{1}{2} \) using the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the general solution for $ heta$ in the equation $sin( heta) = frac{1}{2}$ using the unit circle. Answer 1 Matthew Carter To find the general solution for the equation $sin(theta) = frac{1}{2}$, we use the unit circle. On the unit circle, $sin(theta) =...

Find the coordinates of a point on the unit circle at an angle of 45 degrees

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the coordinates of a point on the unit circle at an angle of $45^{circ}$ Answer 1 Christopher Garcia To find the coordinates of a point on the unit circle at an angle of $45^{circ}$, we use the sine and cosine functions.First, we convert the angle to...

Find the Exact Values of Trigonometric Functions for Given Angles

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the Exact Values of Trigonometric Functions for Given Angles Answer 1 Emily Hall Given the angle $theta = frac{5pi}{6}$, find the exact values of $sin theta$, $cos theta$, and $tan theta$ using the unit circle. First, determine the reference angle for $theta...

Find the sine and cosine values for an angle of 5π/4 radians on the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the sine and cosine values for an angle of $frac{5pi}{4}$ radians on the unit circle. Answer 1 Ava Martin To find the sine and cosine values for an angle of $frac{5pi}{4}$ radians, we need to locate this angle on the unit circle.First, we recognize that...

Determine the Quadrant of Multiple Angles on the Unit Circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Determine the Quadrant of Multiple Angles on the Unit Circle Answer 1 Daniel Carter Given the angles $30^circ$, $150^circ$, and $240^circ$, determine the quadrant each angle lies in on the unit circle. 1. For $30^circ$, it is in the first quadrant because it is...

Determine the coordinates of a point on the unit circle given a specific angle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Determine the coordinates of a point on the unit circle given a specific angle. Answer 1 James Taylor Given an angle ( theta = frac{5pi}{6} ), find the coordinates of the corresponding point on the unit circle.1. The angle ( frac{5pi}{6} ) is in the second...