by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home $Find the coordinates of a point on the unit circle given an angle in radians$ Answer 1 Samuel Scott Given an angle $theta = frac{pi}{3}$ radians, find the coordinates of the point on the unit circle.The unit circle is defined by the equation $x^2 + y^2 = 1$. For...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home ”Find Answer 1 Benjamin Clark To solve for $theta$ in $cot(theta) = frac{1}{sqrt{3}}$, we start by recalling the definition of cotangent:$cot(theta) = frac{1}{tan(theta)}$Given $cot(theta) = frac{1}{sqrt{3}}$, we have:$frac{1}{tan(theta)} =...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the value of $ an( heta)$ on the unit circle where $ heta=150^circ$ Answer 1 Maria Rodriguez To find $tan(150^circ)$, we first note that $150^circ$ can be written as $180^circ – 30^circ$. The reference angle here is $30^circ$. Since $tantheta$ is...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the coordinates on the unit circle for an angle of $frac{pi}{3}$ radians. Answer 1 Henry Green To find the coordinates of an angle of $frac{pi}{3}$ radians on the unit circle, we use the cosine and sine values of the angle.The cosine of $frac{pi}{3}$ is...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the values of $cos( heta)$ and $sin( heta)$ for $ heta = frac{5pi}{4}$ Answer 1 John Anderson To find the values of $cos(theta)$ and $sin(theta)$ for $theta = frac{5pi}{4}$, we start by locating the angle on the unit circle. The angle $frac{5pi}{4}$ is in...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Find the cosine of an angle using the unit circle in the complex plane Answer 1 Henry Green Given an angle ( theta ) in the complex plane, the unit circle can be used to find the cosine of the angle. The cosine of the angle ( theta ) is the x-coordinate of the...
by zhanhongyuan | Feb 8, 2025 | Unit Circle
Home Convert the point on the unit circle given in Cartesian coordinates $(sqrt{3}/2, 1/2)$ to its corresponding angle in degrees and radians, and verify the solution by converting the angle back to Cartesian coordinates. Answer 1 James Taylor We are given the point...
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...