What is the y-coordinate of the point on the unit circle at an angle of π/3?

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home What is the y-coordinate of the point on the unit circle at an angle of $frac{pi}{3}$? Answer 1 Sophia Williams To find the y-coordinate of the point on the unit circle at an angle of $frac{pi}{3}$, we use the sine function.The sine of $frac{pi}{3}$ is...

Determine the sine and cosine of the angle π/4 on the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Determine the sine and cosine of the angle $frac{pi}{4}$ on the unit circle. Answer 1 Ava Martin To find the sine and cosine of the angle $frac{pi}{4}$ on the unit circle, we use the definitions of sine and cosine for the unit circle.For an angle $theta$ in the...

Given a point on the unit circle at an angle of 3π/4 radians, find the coordinates of this point and verify the trigonometric identities for sine and cosine at this angle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Given a point on the unit circle at an angle of $frac{3pi}{4}$ radians, find the coordinates of this point and verify the trigonometric identities for sine and cosine at this angle. Answer 1 Thomas Walker To solve this problem, we first need to understand the...

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...