Ai Tools

Answer 1 Answer 1: Given an angle \( \theta \) in the unit circle, we need to find the value of \( \csc(\theta) \). Recall that \( \csc(\theta) = \frac{1}{\sin(\theta)} \). Let's consider \( \theta = \frac{5\pi}{6} \). First, we find \(...

Answer 1 To find $\cot \left( \frac{\pi}{4} \right)$, we use the definition of cotangent in terms of sine and cosine.$\cot \theta = \frac{\cos \theta}{\sin \theta}$For $\theta = \frac{\pi}{4}$, we have:$\cos \left( \frac{\pi}{4} \right) =...

Answer 1 We must first determine the reference angle for $ \frac{5\pi}{6} $. This angle is in the second quadrant. The reference angle for $ \frac{5\pi}{6} $ is $ \pi - \frac{5\pi}{6} = \frac{\pi}{6} $. In the second quadrant, the cosine function is...

Answer 1 To find the equations of all circles on the unit circle, we start with the general form of a circle's equation:$ (x - h)^2 + (y - k)^2 = r^2$Since we are dealing with the unit circle, the radius r is 1. Thus, the equation simplifies to:$ (x...

Answer 1 To find the value of $\tan(\theta)$ where $\theta$ is a special angle on the unit circle, we use the definition $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. For $\theta = \frac{\pi}{4}$, the sine and cosine values are both...