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...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Evaluate the integral of $ cos(x)sin(x) $ from $ 0 $ to $ frac{pi}{2} $ Answer 1 Emma Johnson To evaluate the integral of $ cos(x)sin(x) $ from $ 0 $ to $ frac{pi}{2} $, we can use the substitution method. Let:$ u = sin(x) $Then,$ du = cos(x) dx $The integral...
by zhanhongyuan | Feb 2, 2025 | Unit Circle
Home Explain how to derive the sine and cosine values of standard angles using the unit circle. Answer 1 Lucas Brown To derive the sine and cosine values of standard angles (0°, 30°, 45°, 60°, and 90°) using the unit circle, follow these steps:1. Draw the unit circle...