Answer 1 Given a point $P(x, y)$ on the unit circle: $x = \cos(\theta), \quad y = \sin(\theta)$ The cotangent of angle $\theta$ is: $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ Since $x = \cos(\theta)$ and $y = \sin(\theta)$, we can write:...

Answer 1 Given an angle \( \theta \) in radians, find the coordinates of the corresponding point on the unit circle. Step 1: Recall the unit circle definition. The unit circle is a circle with a radius of 1 centered at the origin \((0, 0)\) in the...

Answer 1 Consider the unit circle defined by the equation $x^2 + y^2 = 1$ and the line with the equation $y = mx + c$.To find the intersection points, substitute $y = mx + c$ into the unit circle's equation:$x^2 + (mx + c)^2 = 1$Expand and...

Answer 1 For an angle \(\theta = \frac{\pi}{4}\) on the unit circle, we use the trigonometric functions sine and cosine to find the coordinates. The coordinates are given by \((\cos \theta, \sin \theta)\). $ \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} $...