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Answer 1 First, recall that for any point on the unit circle, its coordinates can be represented as \((x, y) = (\cos \theta, \sin \theta)\). Given an angle \(\theta = \frac{3\pi}{4}\), we can calculate the coordinates as follows: $ x = \cos \left(...
Answer 1 To convert 135 degrees to radians, we use the formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$ So, $135 \times \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4}$ Next, we find the sine and cosine values for...
Answer 1 $\text{Given an angle of } \theta = \frac{5\pi}{4}$We know that:$\tan \theta = \frac{\sin \theta}{\cos \theta}$On the unit circle, for \(\theta = \frac{5\pi}{4}, \sin \theta = -\frac{\sqrt{2}}{2} \) and \(\cos \theta =...
Answer 1 First, we need to determine the coordinates of the point on the unit circle corresponding to $\theta = \frac{\pi}{4}$.On the unit circle, the coordinates for the angle $\frac{\pi}{4}$ are $\left(\frac{\sqrt{2}}{2},...
Answer 1 To find $\cos(-\pi/3)$, we first need to understand its position on the unit circle. The angle $-\pi/3$ is equivalent to rotating $\pi/3$ radians in the clockwise direction. On the unit circle, $\pi/3$ radians is located in the first...
Answer 1 To calculate $\tan\left(\frac{4\pi}{3}\right)$, we start by locating the angle $\frac{4\pi}{3}$ on the unit circle. The angle $\frac{4\pi}{3}$ radians is equivalent to $240^\circ$. This angle lies in the third quadrant where both sine and...