sin(3/2 pi)
Understand the Problem
The question is asking for the value of the sine function at the angle of 3/2 pi radians. To solve this, we can evaluate sin(3Ï€/2) using the unit circle or trigonometric identities.
Answer
$ -1 $
Answer for screen readers
The value of $ \sin\left(\frac{3\pi}{2}\right) $ is $ -1 $.
Steps to Solve
- Identify the angle on the unit circle
The angle $ \frac{3\pi}{2} $ radians corresponds to $270^\circ$ in degrees. In the unit circle, this angle points straight down along the negative y-axis.
- Determine the coordinates on the unit circle
At $ \frac{3\pi}{2} $ radians, the coordinates of the point on the unit circle are $(0, -1)$.
- Relate the sine to the coordinates
The sine of an angle in the unit circle is given by the y-coordinate of the corresponding point. Therefore, for $ \frac{3\pi}{2} $, we find:
$$ \sin\left(\frac{3\pi}{2}\right) = -1 $$
The value of $ \sin\left(\frac{3\pi}{2}\right) $ is $ -1 $.
More Information
The sine value of angles can be visualized using the unit circle. The sine function represents the y-coordinate of points on the circle, helping us understand its behavior in different quadrants.
Tips
- Mixing Radians and Degrees: Sometimes students confuse radians with degrees. It's important to keep track of which units you're working with.
- Incorrect Coordinates: Forgetting the coordinates at specific angles can lead to errors in finding sine and cosine values.
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