by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle where the angle is $frac{pi}{10}$ radians. Answer 1 Christopher Garcia To find the coordinates of the point on the unit circle at an angle of $frac{pi}{10}$ radians, we use the cosine and sine functions: $x =...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find all the solutions for $cos( heta) = -frac{1}{2}$ on the unit circle. Answer 1 Joseph Robinson $ text{We need to find all } theta text{ such that } cos(theta) = -frac{1}{2}. $ $ text{The values of } theta text{ where } cos(theta) = -frac{1}{2} text{ are at }...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the value of $cot(45^circ)$ on the unit circle. Answer 1 Amelia Mitchell To find $cot(45^circ)$ on the unit circle, we start by recalling that cotangent is the reciprocal of the tangent function.Given: $cot(theta) = frac{1}{tan(theta)} $For $theta =...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $ ext{Find the Quadrant of a Given Angle on the Unit Circle}$ Answer 1 Sophia Williams To determine the quadrant in which the angle 150° lies, we first convert it to radians:$150° times frac{pi}{180°} = frac{5pi}{6}$The angle (frac{5pi}{6}) is greater than...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the sine and cosine of the angle at three specific points on the unit circle. Answer 1 Mia Harris The three specific points we will consider are $frac{pi}{6}$, $frac{pi}{4}$, and $frac{pi}{3}$. 1. For $frac{pi}{6}$: The sine value can be found using the unit...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $ ext{Given a point on the unit circle at coordinates } (sqrt{3}/2, -1/2), ext{ find the angle in radians, the corresponding angle in degrees, and the sine of the angle.}$ Answer 1 Charlotte Davis To find the angle in radians, we use the coordinates on the unit...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the sine, cosine, and tangent of $frac{pi}{6}$ on the unit circle. Answer 1 Sophia Williams To find the sine, cosine, and tangent of $frac{pi}{6}$, we use the unit circle values: Sine of $frac{pi}{6}$: $sinleft(frac{pi}{6}right) = frac{1}{2}$ Cosine of...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Given a point ((x,y)) on the unit circle where the angle in radians is $ heta$, express the coordinates of the point in terms of $cos( heta)$ and $sin( heta)$, and show how these expressions can be derived from the Pythagorean identity. Additionall Answer 1...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the value of $sin$, $cos$, and $ an$ for $45^circ$ using the unit circle. Answer 1 Isabella Walker To find the values of $sin$, $cos$, and $tan$ for $45^circ$ using the unit circle, we first note that $45^circ$ is equivalent to $frac{pi}{4}$ radians.On the...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $ ext{Consider a unit circle with center at the origin. A square is inscribed in the circle, and a triangle is inscribed in the square. Determine the area of the triangle.}$ Answer 1 Lucas Brown $text{First, determine the side length of the square inscribed in...