by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $ arcsin(frac{1}{2}) $ in radians using the unit circle. Answer 1 William King To find the value of $ arcsin(frac{1}{2}) $, consider the unit circle and the definition of arcsin. The arcsin function outputs the angle whose sine is the given...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the value of $cosleft(frac{3pi}{4} ight)$. Answer 1 Alex Thompson The unit circle helps us locate the angle $theta = frac{3pi}{4}$ which lies in the second quadrant. The reference angle for $theta = frac{3pi}{4}$ is: $pi – frac{3pi}{4} = frac{pi}{4}$...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle Answer 1 Benjamin Clark To find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle, we use the unit circle definition. The unit...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home How to find the reference angle for any angle not on the unit circle Answer 1 Charlotte Davis To find the reference angle for an angle θ not on the unit circle, you must first locate the angle in the appropriate quadrant. The reference angle is then the smallest...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Given that $ cos(θ) = -frac{1}{2} $, find the general solutions for $ θ $ in the unit circle. Answer 1 Emma Johnson To solve for $ θ $ such that $ cos(θ) = -frac{1}{2} $, we need to find all angles in the unit circle where the cosine value is $ -frac{1}{2} $. The...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home How to memorize the coordinates of the unit circle Answer 1 Mia Harris One method to memorize the unit circle is to remember key angles in radians and their corresponding coordinates. For example,: $ text{At } theta = 0, (1, 0) $ $ text{At } theta = frac{pi}{2},...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Prove that the integral of $ frac{sin(x)}{x} $ from $ 0 $ to $ infty $ is $ frac{pi}{2} $ Answer 1 Lucas Brown To prove that the integral of $ frac{sin(x)}{x} $ from $ 0 $ to $ infty $ is $ frac{pi}{2} $, we will use the fact that:$ int_0^infty frac{sin(x)}{x} ,...
by zhanhongyuan | Feb 2, 2025 | Math
Home Find the equation of the circle that passes through the points $ A(1, 2) $, $ B(4, 6) $, and $ C(-3, -5) $ Answer 1 Lily Perez To find the equation of the circle passing through the points $ A(1, 2) $, $ B(4, 6) $, and $ C(-3, -5) $, we can use the determinant...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Solve for all $x$ given that $sin(x) + cos(2x) = 1$, where $x$ is an angle on the unit circle. Answer 1 John Anderson To solve for all $x$ given that $sin(x) + cos(2x) = 1$:First, use the double-angle identity for cosine: $cos(2x) = 2cos^2(x) – 1$Substitute...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Determine the exact value of a trigonometric expression involving radians on the unit circle Answer 1 Lucas Brown Consider the trigonometric expression $ cosleft(frac{7pi}{4}right) + sinleft(frac{7pi}{4}right) $. Determine its exact value using the unit...