by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the sine, cosine, and tangent values for the angle $ heta = frac{5pi}{6}$ using the unit circle. Answer 1 William King For the angle $theta = frac{5pi}{6}$: The reference angle is $pi – frac{5pi}{6} = frac{pi}{6}$. In the second quadrant, sine is...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home $Ways to Memorize the Unit Circle$ Answer 1 Isabella Walker $Ways to Memorize the Unit Circle$Explanation with Examples:The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. To memorize the unit circle, follow these...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle corresponding to a given angle Answer 1 Emma Johnson Given an angle of ( theta = 45^{circ} ). To find the coordinates of the point on the unit circle:The coordinates of any point on the unit circle can be found...
by zhanhongyuan | Feb 10, 2025 | Math
Home Find the circumference of a circle with a radius of $4$ units. Answer 1 Christopher Garcia To find the circumference of a circle, we use the formula: $ C = 2pi r $ Given that the radius ( r = 4 ) units, we substitute this value into the formula: $ C = 2 pi times...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the value of $ an( heta)$ on the unit circle where $ heta$ is $frac{pi}{4}$. Answer 1 Mia Harris On the unit circle, the coordinates for $theta = frac{pi}{4}$ are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2} right)$. Therefore, $tan(frac{pi}{4})$ is calculated...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home If point $P$ on the unit circle is flipped over the $y$-axis, what will be the coordinates of point $P$ if it initially lies on the point $(frac{sqrt{3}}{2}, frac{1}{2})$? Answer 1 Mia Harris Initial coordinates of point $P$ are $(frac{sqrt{3}}{2}, frac{1}{2})$....
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the coordinates of a point on the unit circle at $45^{circ}$. Answer 1 William King The unit circle is a circle with a radius of 1 centered at the origin. To find the coordinates of a point at $45^{circ}$, we use the trigonometric functions sine and...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the coordinates of the points on the unit circle where the angle formed with the positive x-axis is such that the cosine of the angle equals $frac{-3}{5}$. Additionally, find the corresponding sine value. Answer 1 Amelia Mitchell To solve this problem, we...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the Cartesian coordinates of a point on the unit circle where the angle is $135^{circ}$. Answer 1 Alex Thompson To find the Cartesian coordinates of a point on the unit circle where the angle is $135^{circ}$, we use the unit circle equation:$x =...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the exact value of $ sin(2 heta) $ and $ cos(2 heta) $ given the point on the unit circle and the quadrant Answer 1 Sophia Williams Given the point $ P = left( -frac{3}{5}, -frac{4}{5} right) $ on the unit circle, find the exact values of $ sin(2theta) $ and...