Answer 1 First, we need to determine the reference angle for $\frac{5\pi}{6}$. The reference angle is $\pi - \frac{5\pi}{6} = \frac{\pi}{6}$. In the second quadrant, sine is positive and cosine is negative. The sine value for $\frac{\pi}{6}$ is...

Answer 1 Given an angle $\theta$, find the values of $\sin(\theta)$ and $\cos(\theta)$ using the unit circle equation. Suppose $\theta = \frac{\pi}{4}$.The unit circle equation is given by:$x^2 + y^2 = 1$For $\theta = \frac{\pi}{4}$, the...

Answer 1 The angle $\frac{\pi}{3}$ corresponds to 60 degrees on the unit circle. The coordinates of this angle on the unit circle are $(\frac{1}{2}, \frac{\sqrt{3}}{2})$. Therefore, the cosine of the angle $\frac{\pi}{3}$ is $\frac{1}{2}$, and the...

Answer 1 To find the coordinates of the point on the unit circle corresponding to an angle of $\frac{5\pi}{6}$, we can use the sine and cosine functions. The angle $\frac{5\pi}{6}$ is in the second quadrant.The reference angle is $\pi -...

Answer 1 To find the sine and cosine of the angle $\theta = 45°$, we use the unit circle where the radius is 1. The coordinates of the point where the terminal side of a 45° angle intersects the unit circle are $\left(\frac{\sqrt{2}}{2},...