Find the tangent values at 0, π/4, and π/2 on the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the tangent values at $ 0 $, $ frac{pi}{4} $, and $ frac{pi}{2} $ on the unit circle Answer 1 Ella Lewis To find the tangent values at specific points on the unit circle, we use the definition of the tangent function, which is $ tan(theta) =...

Find the coordinates of the point on the unit circle where the angle is pi over 4 radians

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle where the angle is $ frac{pi}{4} $ radians Answer 1 Lucas Brown To find the coordinates of the point on the unit circle where the angle is $ frac{pi}{4} $ radians, we use the unit circle definition:The...

Identify the coordinates on the unit circle for angle θ

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Identify the coordinates on the unit circle for angle $ heta $ Answer 1 Amelia Mitchell The coordinates of a point on the unit circle for a given angle $ theta $ are given by:$ ( cos(theta), sin(theta) ) $For example, if $ theta = frac{pi}{4} $:$ (...

Find the values of tan(θ) for θ in the interval [0, 2π] that satisfy the equation tan(θ) = 2

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home ”Find Answer 1 Ella Lewis To find the values of $ tan(theta) $ that satisfy the equation $ tan(theta) = 2 $ in the interval $ [0, 2pi] $, we need to determine the angles where the tangent function equals 2.First, recall that the tangent function is periodic...

Solve the equation to find all distinct points where the ellipse intersects the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Solve the equation to find all distinct points where the ellipse intersects the unit circle Answer 1 Michael Moore To find where the ellipse $frac{x^2}{a^2} + frac{y^2}{b^2} = 1$ intersects the unit circle $x^2 + y^2 = 1$, we need to solve the system of...

Determine the sine and cosine values of 5π/6

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Determine the sine and cosine values of $ frac{5pi}{6} $ Answer 1 John Anderson To determine the sine and cosine values of $ frac{5pi}{6} $, we refer to the unit circle.The angle $ frac{5pi}{6} $ is located in the second quadrant.In the second quadrant, sine is...

Find the sine and cosine of the angle π/3 using the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the sine and cosine of the angle $ pi/3 $ using the unit circle Answer 1 Emily Hall To find the sine and cosine of the angle $ pi/3 $ using the unit circle, consider the angle that corresponds to $ pi/3 $ radians (or 60 degrees).In the unit circle, the...

Find the coordinates of the point where the terminal side of the angle intersects the unit circle at an angle of 5π/4 radians

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the coordinates of the point where the terminal side of the angle intersects the unit circle at an angle of $frac{5pi}{4}$ radians Answer 1 Emma Johnson To find the coordinates of the point where the terminal side of the angle intersects the unit circle at...

Find the coordinates of cos(π/3) on the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the coordinates of $ cos(frac{pi}{3}) $ on the unit circle Answer 1 Henry Green To find the coordinates of $ cos(frac{pi}{3}) $ on the unit circle, we need to identify the coordinates associated with this angle.On the unit circle, the angle $ frac{pi}{3} $...

Determine the general solution for sin(x) = 1/2 within [0, 2π]

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home ”Determine Answer 1 Chloe Evans To determine the general solution for $ sin(x) = frac{1}{2} $ within the interval $ [0, 2pi] $, we need to find all the angles $ x $ where the sine function yields $ frac{1}{2} $ on the unit circle.The sine function equals $...