by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ cos(frac{pi}{4}) $ on the unit circle. Answer 1 Mia Harris On the unit circle, the angle $ frac{pi}{4} $ corresponds to 45 degrees. The coordinates of this point are ( frac{sqrt{2}}{2}, frac{sqrt{2}}{2} ). Therefore,$ cos(frac{pi}{4}) =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the coordinates of a point on the unit circle given the angle $ heta = frac{pi}{4}$ Answer 1 James Taylor To find the coordinates of a point on the unit circle given the angle $theta = frac{pi}{4}$, we use the definitions of sine and cosine:$ x =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the values of $ sin, cos, $ and $ an $ for an angle of $ frac{pi}{4} $ on the unit circle Answer 1 Matthew Carter To find the values of $ sin, cos, $ and $ tan $ for an angle of $ frac{pi}{4} $ on the unit circle, we start with:$ sinleft(frac{pi}{4}right) =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Calculate the coordinates of a point on the unit circle at an angle of $ frac{5pi}{6} $ Answer 1 Michael Moore To find the coordinates of a point on the unit circle at an angle of $ frac{5pi}{6} $, we use the unit circle properties.In the unit circle, the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ an( heta)$ using the unit circle Answer 1 Matthew Carter To find the value of $tan(theta)$ using the unit circle, we need to know the coordinates of the point on the unit circle that corresponds to the angle $theta$.On the unit circle, the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the values of $ an( heta) $ on the unit circle where $ an( heta) = 1 $ or $ an( heta) = -1 $ Answer 1 Ella Lewis First, note that $ tan(theta) = 1 $ when $ theta = frac{pi}{4} $ or $ theta = frac{5pi}{4} $ on the unit circle. Also, $ tan(theta) = -1 $...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the value of $ arctan(sin(frac{3pi}{4})) $ Answer 1 Emma Johnson To find the value of $ arctan(sin(frac{3pi}{4})) $, we first need to find the value of $ sin(frac{3pi}{4}) $.$ sin(frac{3pi}{4}) = sin(pi – frac{pi}{4}) = sin(frac{pi}{4}) =...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle with the positive $x$-axis is $frac{pi}{3}$ Answer 1 Amelia Mitchell The unit circle is defined as a circle with radius 1 centered at the origin. The coordinates of any point on the unit circle...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the coordinates of the point where the terminal side of an angle $ heta$ intersects the unit circle, given that $ heta = frac{5pi}{6}$ Answer 1 Sophia Williams To determine the coordinates where the terminal side of $theta = frac{5pi}{6}$ intersects the unit...
by zhanhongyuan | Feb 3, 2025 | Math
Home Calculate the area of a sector of a circle with radius $ r $ and central angle $ heta $ (in radians) Answer 1 Maria Rodriguez The area of a sector of a circle with radius $ r $ and central angle $ theta $ can be calculated using the formula:$ A = frac{1}{2} r^2...