by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Given a point on the unit circle, determine the coordinates and verify the trigonometric identities. Answer 1 Lily Perez Let’s consider a point $P(costheta, sintheta)$ on the unit circle where $theta = frac{5pi}{6}$. To find the coordinates and verify...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home $ ext{What is the cosine of the angle } frac{pi}{3} ext{ on the unit circle?}$ Answer 1 Sophia Williams To find the cosine of the angle ( frac{pi}{3} ) on the unit circle, we need to locate this angle on the circle. The angle ( frac{pi}{3} ) corresponds to 60...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find all angles $ heta$ between Define the unit circle in trigonometry$ and $2pi$ such that $cos( heta) = -frac{1}{2}$ Answer 1 Mia Harris To find the angles $theta$ such that $cos(theta) = -frac{1}{2}$, we start by identifying the quadrants where $cos(theta)$ is...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle at an angle of $45^{circ}$ from the positive x-axis. Answer 1 Christopher Garcia To find the coordinates of a point on the unit circle, we use the trigonometric functions sine and cosine.The angle given is...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the value of $x$ such that $cos(x) = -frac{1}{2}$ and $sin(x)$ is negative on the unit circle. Answer 1 Abigail Nelson To solve for $x$ such that $cos(x) = -frac{1}{2}$ and $sin(x)$ is negative on the unit circle, follow these steps: 1. Identify the angles...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the exact values of sine and cosine for the angle $frac{5pi}{4}$ using the unit circle. Answer 1 Ava Martin To find the exact values of sine and cosine for the angle $frac{5pi}{4}$, we start by determining in which quadrant the angle lies. The angle...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Given the point $P$ on the unit circle at an angle of $210^{circ}$, find $cos(210^{circ})$ and $sin(210^{circ})$. Answer 1 Chloe Evans To find $cos(210^{circ})$ and $sin(210^{circ})$, we start by converting the angle to radians:$210^{circ} = 210 cdot...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home $ ext{Find the coordinates of the points where the unit circle intersects the x-axis.}$ Answer 1 Christopher Garcia $text{The unit circle has the equation } x^2 + y^2 = 1.$$text{To find the intersection with the x-axis, we set } y = 0.$$x^2 + 0^2 = 1$$x^2 = 1$$x...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Given a point $P$ on the unit circle at an angle $ heta$, find the coordinates of $P$, the length of the line segment from $P$ to the origin, and the area of the sector formed by the angle $ heta$ in the unit circle. Answer 1 Thomas Walker Given a point $P$ on...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home $Find the angle that corresponds to a given point on the unit circle.$ Answer 1 Ella Lewis Let’s consider the point (frac{sqrt{3}}{2}, , frac{1}{2}) on the unit circle. This point lies in the first quadrant and has coordinates (cos(theta), sin(theta)). We...