by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home $Convert the angle 150^{circ} to radians and find its coordinates on the unit circle.$ Answer 1 Alex Thompson To convert degrees to radians, we use the conversion factor ( frac{pi}{180} ).$150^{circ} times frac{pi}{180} = frac{150pi}{180} = frac{5pi}{6}$The...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home If $ heta$ is an angle in the unit circle such that $cos( heta) = frac{1}{2}$ and $sin( heta) = frac{sqrt{3}}{2}$, find the value of $ heta$ in degrees and radians. Answer 1 Lucas Brown To solve this problem, we need to determine the angle $theta$ on the unit...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the sine and cosine values at different points on the unit circle. Answer 1 Lily Perez To find the sine and cosine values at different points on the unit circle, we can use the angle in radians.1. For the angle $frac{pi}{6}$ radians: The coordinates on the...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the exact value of $cos(frac{5pi}{6})$ using the unit circle. Answer 1 Emily Hall To find the exact value of $cos(frac{5pi}{6})$, we first determine the location of the angle on the unit circle.The angle $frac{5pi}{6}$ is in the second quadrant. In the unit...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the coordinates of the point on the unit circle at an angle of $240^circ$. Answer 1 Emma Johnson First, we convert 240 degrees to radians since the unit circle is often used with radians. The conversion factor is $pi$ radians = 180 degrees.Thus, $240^circ =...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the value of $cos(frac{pi}{4})$ Answer 1 William King To find the value of $cos(frac{pi}{4})$, we must understand the unit circle. The angle $frac{pi}{4}$, or 45 degrees, is a special angle in the unit circle.The coordinates of the point where the terminal...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Find the angle on the unit circle corresponding to the coordinates $left(-frac{2}{3}, y ight)$. Answer 1 John Anderson To find the angle on the unit circle corresponding to the coordinates $left(-frac{2}{3}, yright)$, we need to use the Pythagorean identity:$x^2...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home $ ext{Properties and Implications of the Unit Circle}$ Answer 1 Thomas Walker $text{A unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. To understand its properties, consider a point } (x, y) text{ on the unit circle....
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home $ ext{How to find reference angle not on unit circle}$ Answer 1 Daniel Carter Given an angle of 210 degrees, find the reference angle.Step 1: Determine the quadrant in which the angle lies. 210 degrees is in the third quadrant.Step 2: Use the formula for finding...
by zhanhongyuan | Feb 11, 2025 | Unit Circle
Home Given the unit circle, find the angles $ heta$ between Define the unit circle in trigonometry$ and $2pi$ for which the secant function $sec( heta)$ equals 2, and provide a step-by-step explanation for your answer. Answer 1 Olivia Lee We start by recalling the...