Answer 1 To find the sine and cosine values of $\frac{\pi}{4}$ using the unit circle, follow these steps:1. Identify the angle $\frac{\pi}{4}$ on the unit circle. This angle corresponds to 45 degrees.2. For the angle $\frac{\pi}{4}$, both the...

Answer 1 $\text{Given the unit circle, we need to find the value of } \cos(\theta) \text{ where } \theta \text{ is an angle such that } 2\cos^2(\theta) + \cos(\theta) - 1 = 0.$ $\text{Step 1: Solve the quadratic equation} $ $2\cos^2(\theta) +...

Answer 1 To find the cosine and sine of the angle $ \frac{5\pi}{6} $, we can use the unit circle. The angle $ \frac{5\pi}{6} $ is in the second quadrant, where the cosine is negative and the sine is positive.First, find the reference angle: $...

Answer 1 First, we need to recognize that the angle $\frac{\pi}{4}$ is equivalent to 45 degrees.On the unit circle, the coordinates at $\frac{\pi}{4}$ are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.The sine value is the...

Answer 1 First, understand that on the unit circle, a point corresponding to an angle $\theta$ can be represented as $e^{i\theta} = \cos(\theta) + i\sin(\theta)$. For $\theta = \frac{\pi}{3}$, $e^{i\frac{\pi}{3}} = \cos\left(\frac{\pi}{3}\right) +...