Answer 1 The negative unit circle is described by the equation:$ x^2 + y^2 = -1 $To find where the tangent line is vertical, we need to find the points where the derivative of $ y $ with respect to $ x $ is undefined. First, implicitly differentiate...

Answer 1 On the unit circle, any point is represented as $(\cos(\theta), \sin(\theta))$, where $\theta$ is the angle formed with the positive x-axis.According to the Pythagorean theorem, the equation of the unit circle is:$ x^2 + y^2 = 1...

Answer 1 For the angle $ \frac{\pi}{3} $ on the unit circle, the coordinates are found using the sine and cosine functions.The x-coordinate is:$ \cos\left( \frac{\pi}{3} \right) = \frac{1}{2} $The y-coordinate is:$ \sin\left( \frac{\pi}{3} \right) =...

Answer 1 To determine the value of $ \cos\left(\frac{7\pi}{6}\right) $ using the unit circle, we need to locate the angle $ \frac{7\pi}{6} $ in radians. This angle is in the third quadrant.In the third quadrant, the cosine function is negative. The...

Answer 1 To find the sine and cosine of $ \frac{5\pi}{6} $ on the unit circle, we use the reference angle and the fact that it lies in Quadrant II:The reference angle for $ \frac{5\pi}{6} $ is $ \pi - \frac{5\pi}{6} = \frac{\pi}{6} $.In Quadrant II,...