by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the exact values of $sin( heta)$ and $cos( heta)$ for $ heta = frac{5pi}{6}$ using the unit circle. Answer 1 Emily Hall To find the exact values of $sin(theta)$ and $cos(theta)$ for $theta = frac{5pi}{6}$, we use the unit circle. The angle $frac{5pi}{6}$...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Convert $120^{circ}$ to radians using the unit circle. Answer 1 James Taylor To convert degrees to radians, use the formula: $text{radians} = text{degrees} times frac{pi}{180}$ Plugging in 120 degrees: $120^{circ} times frac{pi}{180} = frac{120pi}{180}$ Simplify...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Derivation and Memorization Techniques for the $Unit Circle$ Answer 1 Maria Rodriguez In order to memorize the unit circle, one effective method is to understand how it is derived from fundamental trigonometric principles. Let’s start by deriving key...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the sine, cosine, and tangent values of the angle $225^{circ}$ using the unit circle Answer 1 Abigail Nelson To find the sine, cosine, and tangent values of the angle $225^{circ}$ using the unit circle, follow these steps:1. Convert the angle to radians:...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home What is the sine of 45 degrees in the unit circle? Answer 1 Alex Thompson First, we need to remember that the unit circle has a radius of 1 and it is centered at the origin (0,0).To find the sine of 45 degrees, we use the coordinates of the point where the...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home What is the sine value of an angle of $frac{pi}{4}$ radians on the unit circle? Answer 1 Daniel Carter To find the sine value of an angle of $frac{pi}{4}$ radians on the unit circle, we use the unit circle properties. The angle $frac{pi}{4}$ radians is equivalent...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Find the value of $ an( heta)$ given a point on the unit circle Answer 1 Benjamin Clark Given a point on the unit circle at coordinates $(x, y)$, find the value of $tan(theta)$ where $theta$ is the angle formed by the radius connecting the point to the...
by zhanhongyuan | Feb 10, 2025 | Unit Circle
Home Determine the Quadrant on a Unit Circle Answer 1 Olivia Lee To determine the quadrant of the angle $( theta )$ on the unit circle, we need to understand the angle’s position in relation to the x-axis and y-axis. Consider the angle $( theta = 150^{circ} )$....
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home $ ext{Find the value of cosine for an angle on the unit circle}$ Answer 1 Mia Harris Let’s find the value of $cos(frac{pi}{4})$ on the unit circle. The angle $frac{pi}{4}$ is equivalent to 45 degrees. On the unit circle, the coordinates of the point at an angle...
by zhanhongyuan | Feb 9, 2025 | Unit Circle
Home Given a point $P$ on the unit circle such that its coordinates are $(cos( heta), sin( heta))$, find the coordinates of the point $Q$, which is the reflection of $P$ across the line $y = x$. Then, find the coordinates of the point $R$, which is the refle Answer 1...