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Answer 1 To find the exact value of $\sin(\frac{5π}{6})$, we first determine the corresponding angle in degrees. Converting radians to degrees:$\frac{5π}{6} \times \frac{180^\circ}{π} = 150^\circ$Now, considering the unit circle, the angle...
Answer 1 To find the sine of $\frac{\pi}{6}$ on the unit circle, we need to know the coordinates of the point on the unit circle corresponding to this angle. The unit circle has a radius of 1, and an angle of $\frac{\pi}{6}$ corresponds to 30 degrees...
Answer 1 To solve this problem, we need to find the coordinates of point $P$ on the unit circle given that the angle $\theta$ is an irrational multiple of $\pi$. Let's denote this angle as $\theta = k\pi$ where $k$ is an irrational number.Using the...
Answer 1 Using the unit circle, we can determine the sine and cosine values of $45^\circ$. $45^\circ$ (or $\frac{\pi}{4}$ radians) is a commonly known angle. The coordinates of the point on the unit circle corresponding to $45^\circ$ are...
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...