by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the equation of the inverse of the unit circle Answer 1 Lucas Brown The equation of the unit circle is:n $ x^2 + y^2 = 1 $n To find the inverse, we use the transformation:n $ z = x0crac{1}{x + yi} $n where $ z = u + vi $ and $ x + yi = x0crac{1}{u –...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the values of $ arcsin( frac{1}{2} ) $ using the unit circle Answer 1 Michael Moore To find the values of $ arcsin( frac{1}{2} ) $ using the unit circle, we look for the angles $ theta $ whose sine value is $ frac{1}{2} $.On the unit circle, the sine value...
by zhanhongyuan | Feb 3, 2025 | Math
Home Find the area of a sector with a central angle of $ heta $ in a unit circle Answer 1 Thomas Walker To find the area of a sector with a central angle of $ theta $ in a unit circle, we use the formula: $ A = frac{1}{2} r^2 theta $ Since it is a unit circle, the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Determine the cosine of an angle on the unit circle at $45^{circ}$ Answer 1 Chloe Evans To find the cosine of an angle at $45^{circ}$ on the unit circle, recall that:$ cos(45^{circ}) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2} $ Answer 2 Ella Lewis To determine the...
by zhanhongyuan | Feb 3, 2025 | Unit Circle
Home Find the exact values of $ an( heta) $ for $ heta $ on the unit circle at each 30-degree increment, and explain the symmetry properties of the tangent function on the unit circle. Answer 1 James Taylor For each 30-degree increment ($ theta $) on the unit circle,...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the exact values of trigonometric functions for given unit circle angles Answer 1 Olivia Lee Given the angle $ theta = frac{5pi}{4} $, find the exact values of $ sin(theta) $, $ cos(theta) $, and $ tan(theta) $:$ sinleft(frac{5pi}{4}right) =...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $ an(frac{pi}{4}) $ on the unit circle Answer 1 Maria Rodriguez To find the value of $ tan(frac{pi}{4}) $ on the unit circle, we use the definition of tangent, which is the ratio of sine to cosine:$ tan(theta) = frac{sin(theta)}{cos(theta)} $At...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the angles at which $ sin( heta) = cos( heta) $ Answer 1 Ava Martin To find the angles where $ sin(theta) = cos(theta) $, we know that:$ sin(theta) = cos(theta) $Dividing both sides by $ cos(theta) $, we get:$ tan(theta) = 1 $Thus, $ theta $ must be an angle...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the sine value at an angle of $ frac{pi}{4} $ on the unit circle Answer 1 Chloe Evans To determine the sine value at an angle of $ frac{pi}{4} $ on the unit circle, recall that at this angle, the coordinates are:$ ( frac{sqrt{2}}{2}, frac{sqrt{2}}{2} )...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine $ an( heta) $ from the unit circle at point $ P(x,y) $ Answer 1 Isabella Walker To determine $ tan(theta) $ from the unit circle at point $ P(x,y) $, recall that$ tan(theta) = frac{sin(theta)}{cos(theta)} $On the unit circle, you have $ P(x,y) =...