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Answer 1 Given the angle $ \theta = \frac{2\pi}{3} $ radians, calculate $ \sin(\theta) $, $ \cos(\theta) $, and $ \tan(\theta) $. Solution: First convert the angle to degrees to understand its position on the unit circle: $\theta = \frac{2\pi}{3} $...
Answer 1 To find the value of $\csc(\theta + i \phi)$ on the unit circle, we first recall that $\csc(z) = \frac{1}{\sin(z)}$ and we utilize the definition of the sine function for complex arguments.Given $z = \theta + i \phi$, we have: $\sin(z) =...
Answer 1 To find the sine and cosine values for the angle $\frac{\pi}{4}$ on the unit circle, we use the fact that the unit circle has a radius of 1 and the coordinates of the point on the unit circle corresponding to this angle are $(\cos\theta,...
Answer 1 We know that the coordinates of a point on the unit circle are given by $(\cos(\theta), \sin(\theta))$. Given $\theta = \frac{\pi}{4}$: $\cos\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$ $\sin\left( \frac{\pi}{4} \right) =...
Answer 1 To find the values of $\sin(\frac{\pi}{4})$ and $\cos(\frac{\pi}{4})$ on the unit circle, we use the coordinates of the point on the unit circle corresponding to the angle $\frac{\pi}{4}$. The angle $\frac{\pi}{4}$ radians corresponds to 45...
Answer 1 $\text{To learn the unit circle, start by understanding that it is a circle with a radius of 1 centered at the origin (0,0).}$ $\text{1. Memorize the key angles: 0°, 30°, 45°, 60°, 90°, and their equivalents in radians.}$ $\text{2. Know the...