Answer 1 $ \text{Given an angle } \theta \text{, we need to find } \cos(\theta) \text{ using the unit circle in the complex plane.} $ $ \text{On the unit circle, the coordinates of a point } P \text{ corresponding to the angle } \theta \text{ are }...

Answer 1 To determine the quadrant of the point $(0.5, 0.5)$ on the unit circle, we need to consider the signs of the x and y coordinates.Both $x = 0.5$ and $y = 0.5$ are positive.Therefore, the point $(0.5, 0.5)$ lies in the first quadrant.Answer 2...

Answer 1 To find the value of $\sec(\frac{\pi}{3})$, we need to first determine the cosine of $\frac{\pi}{3}$. On the unit circle, $\cos(\frac{\pi}{3}) = \frac{1}{2}$. The secant function is the reciprocal of the cosine function, so...

Answer 1 The general equation of a circle with center $(h, k)$ and radius $r$ is given by:$ (x - h)^2 + (y - k)^2 = r^2 $For a unit circle, the radius $r = 1$. Therefore, the equation becomes:$ (x - h)^2 + (y - k)^2 = 1 $Answer 2 The equation of a...