Given the unit circle and the periodic function $f(\theta) = \sin(\theta)$, find the values of $\theta$ for which $\sin(\theta) = \frac{\sqrt{2}}{2}$ in the interval $[0, 2\pi)$ Provide a detailed solution

by | Feb 10, 2025 | Unit Circle

Home ”Given Answer 1 Abigail Nelson Consider the given equation:$sin(theta) = frac{sqrt{2}}{2}$We know that $sin(theta) = frac{sqrt{2}}{2}$ at $theta = frac{pi}{4} + 2npi$ and $theta = frac{3pi}{4} + 2npi$ for any integer $n$.To find the solutions in the...

Find the value of sin(45°) using the unit circle

by | Feb 10, 2025 | Unit Circle

Home Find the value of $sin(45°)$ using the unit circle. Answer 1 Amelia Mitchell First, we need to locate the angle 45° on the unit circle. The coordinates of this angle on the unit circle are (√2/2, √2/2). The sine of the angle is the y-coordinate of the point on...

Find the value of cos(-π/3) on the unit circle

by | Feb 10, 2025 | Unit Circle

Home Find the value of $cos(-pi/3)$ on the unit circle Answer 1 Henry Green To find the value of $cos(-pi/3)$ on the unit circle, we should first recall the basic properties of the cosine function and the unit circle:1. The cosine function is an even function, meaning...