Find the sine and cosine values for a given angle on the unit circle

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Find the sine and cosine values for a given angle on the unit circle Answer 1 Mia Harris Suppose we need to find the sine and cosine values for the angle $ frac{pi}{4} $ on the unit circle.Step 1: Recognize the angle $ frac{pi}{4} $ on the unit circle.Step 2:...

Determine the sin value from the unit circle and verify identities

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Determine the $sin$ value from the unit circle and verify identities Answer 1 Amelia Mitchell Given the point $P(-frac{1}{2}, -frac{sqrt{3}}{2})$ on the unit circle, determine $sin(theta)$ and verify the identity $sin^2(theta) + cos^2(theta) = 1$: 1. Identify the...

Find the tangent for every angle on the unit circle

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home $ ext{Find the tangent for every angle on the unit circle}$ Answer 1 Ella Lewis To find the tangent for every angle (theta) on the unit circle, we use the definition of tangent, which is the ratio of the sine of the angle to the cosine of the angle.The tangent...

Find the coordinates of the points where the line y = 1/2 intersects the unit circle

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Find the coordinates of the points where the line $y = frac{1}{2}$ intersects the unit circle. Answer 1 Charlotte Davis To find the intersection points of the line $y = frac{1}{2}$ and the unit circle, we start with the equation of the unit circle, which is $x^2...

Given an angle θ in the unit circle where sin(θ) = -1/2 and cos(θ) = -√3/2, find the coordinates (x, y) of the corresponding point on the unit circle Additionally, find the other angle φ in the range [0, 2π] which satisfies the same conditions

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home ”Given Answer 1 Alex Thompson First, recognize that $sin(theta) = -frac{1}{2}$ means that $theta$ corresponds to either $210^circ$ or $330^circ$ in degrees, or $frac{7pi}{6}$ or $frac{11pi}{6}$ in radians. Since $cos(theta) = -frac{sqrt{3}}{2}$, we identify...

Determine the angle in radians and the coordinates on the unit circle for the angle whose cosine is -1/2 in the interval [π, 2π], and find the corresponding sine value and tangent value

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home ”Determine Answer 1 Daniel Carter First, consider the unit circle where the cosine value is $frac{-1}{2}$. In the interval $[pi, 2pi]$, the angle where the cosine is $frac{-1}{2}$ is $frac{4pi}{3}$. To find the corresponding sine value:...

Determine the Quadrant of a Point on the Unit Circle

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home $ ext{Determine the Quadrant of a Point on the Unit Circle}$ Answer 1 Emily Hall $text{To determine the quadrant of a point } (x, y) text{ on the unit circle, first consider the angle } theta text{ in radians.}$$text{For example, if } theta = frac{3pi}{4}, text{...

Find the coordinates of a point on the unit circle where the angle in standard position is given by 7π/6 radians

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Find the coordinates of a point on the unit circle where the angle in standard position is given by $frac{7pi}{6}$ radians. Answer 1 Emily Hall To solve this, recall that an angle of $frac{7pi}{6}$ radians is in the third quadrant.The reference angle for...

Convert the angle 225 degrees to radians, find its coordinates on the unit circle, and determine the sine, cosine, and tangent values

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Convert the angle $225^circ$ to radians, find its coordinates on the unit circle, and determine the sine, cosine, and tangent values. Answer 1 Samuel Scott To convert 225 degrees to radians, we use the conversion factor $frac{pi}{180}$:$225^circ times...

Finding the Cartesian Coordinates from Polar Coordinates on a Unit Circle

by zhanhongyuan | Feb 10, 2025 | Unit Circle

Home Finding the Cartesian Coordinates from Polar Coordinates on a Unit Circle Answer 1 Samuel Scott Given a point on the unit circle with polar coordinates $(r, theta)$, where $r = 1$ and $theta = frac{5pi}{6}$, find the Cartesian coordinates $(x, y)$.First, recall...