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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...
Answer 1 $\text{To memorize the unit circle, observe that it is divided into four quadrants. Each quadrant contains key angles: 0, } \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, \text{ and } 2\pi.$ $\text{For...