by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the angle in radians for the point $(-frac{1}{2}, -frac{sqrt{3}}{2})$ on the unit circle Answer 1 Chloe Evans To find the angle in radians for the point $(-frac{1}{2}, -frac{sqrt{3}}{2})$ on the unit circle, we first identify the coordinates. These...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle with a given angle, $ heta $ Answer 1 Christopher Garcia To determine the coordinates of a point on the unit circle given the angle $ theta $, use the unit circle formulas:$ x = cos(theta) $$ y = sin(theta)...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the length of the arc subtended by a central angle of $ heta $ radians in a unit circle Answer 1 Maria Rodriguez To find the length of the arc subtended by a central angle $ theta $ radians in a unit circle, we use the formula:$ s = r theta $Here, the radius...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the exact value of $ an( heta) $ given that $ sin( heta) = frac{3}{5} $ and $ heta $ is in the second quadrant. Answer 1 Olivia Lee Given that $ sin(theta) = frac{3}{5} $ and $ theta $ is in the second quadrant: Since $ sin(theta) $ is positive in the second...
by zhanhongyuan | Feb 4, 2025 | Unit Circle
Home Find the exact values of $sin(frac{7pi}{6})$, $cos(frac{7pi}{6})$, and $ an(frac{7pi}{6})$ using the unit circle. Answer 1 Matthew Carter To find the exact values of $sin(frac{7pi}{6})$, $cos(frac{7pi}{6})$, and $tan(frac{7pi}{6})$ using the unit circle, we...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the values of $ sin $, $ cos $, and $ an $ for $ 30^circ $ on the unit circle. Answer 1 Emma Johnson For $ 30^circ $ on the unit circle:$ sin(30^circ) = frac{1}{2} $$ cos(30^circ) = frac{sqrt{3}}{2} $$ tan(30^circ) = frac{1}{sqrt{3}} text{ or }...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ an(135^circ) $ using the unit circle Answer 1 Benjamin Clark To find the value of $ tan(135^circ) $ using the unit circle, we need to recall that $ tantheta $ is the ratio of the y-coordinate to the x-coordinate of the point where the terminal...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the vertices of a triangle inscribed in a unit circle given angles $ heta_1, heta_2, heta_3 $ Answer 1 Lily Perez Given the angles $ theta_1, theta_2, theta_3 $ of the vertices of the triangle, the coordinates of the vertices on the unit...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
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by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $sin(2x)$ and $cos(2x)$ on the unit circle Answer 1 Benjamin Clark To find the value of $sin(2x)$ and $cos(2x)$ on the unit circle, we can utilize the double-angle formulas: $ sin(2x) = 2sin(x)cos(x) $ $ cos(2x) = cos^2(x) – sin^2(x) $...