Answer 1 To find the coordinates of a point on the unit circle at a given angle, we use the angle to find the cosine and sine values, which correspond to the x and y coordinates, respectively.For an angle of $45^{\circ}$, we have:$\cos(45^{\circ}) =...

Answer 1 To find the sine of 30 degrees on the unit circle, we need to identify the coordinates of the point on the unit circle corresponding to this angle.In the unit circle, each point is represented as $(\cos \theta, \sin \theta)$. For an angle of...

Answer 1 First, let's convert 45 degrees into radians using the conversion factor $\pi / 180$. $\text{Radians} = 45 \times \frac{\pi}{180} = \frac{\pi}{4}$ On the unit circle, the coordinates corresponding to an angle of $\frac{\pi}{4}$ radians are...

Answer 1 To find $\sin(\theta)$ for $\theta = \frac{7\pi}{6}$, we need to locate the angle on the unit circle.First, note that $\frac{7\pi}{6}$ is in the third quadrant where sine is negative.$\frac{7\pi}{6}$ is $30^\circ$ past $\pi$ (180...

Answer 1 Given a point on the unit circle defined by the angle $\theta$ in radians, find the coordinates of the point where $\theta = \frac{5\pi}{6}$.First, recall that any point on the unit circle is defined by $(\cos \theta, \sin \theta)$. Here...