cos(3π/2)
Understand the Problem
The question is asking for the value of the cosine function at the angle of 3π/2 radians. The cosine function is a basic trigonometric function that can be evaluated using the unit circle.
Answer
The value of $ \cos\left(\frac{3\pi}{2}\right) $ is $ 0 $.
Answer for screen readers
The value of $ \cos\left(\frac{3\pi}{2}\right) $ is $ 0 $.
Steps to Solve
- Identify the Angle in Relation to the Unit Circle
The angle $ \frac{3\pi}{2} $ radians corresponds to 270 degrees, which can be visualized on the unit circle.
- Locate the Position on the Unit Circle
On the unit circle, the angle $ \frac{3\pi}{2} $ lands on the negative y-axis. This point can be denoted as $(0, -1)$.
- Determine the Cosine Value
The cosine function represents the x-coordinate of a point on the unit circle. Since at $ \frac{3\pi}{2} $ the coordinates are $(0, -1)$, the cosine value is:
$$ \cos\left(\frac{3\pi}{2}\right) = 0 $$
The value of $ \cos\left(\frac{3\pi}{2}\right) $ is $ 0 $.
More Information
The value of the cosine function for an angle of $ \frac{3\pi}{2} $ radians is $ 0 $. This angle is significant in trigonometry as it is one of the key angles located on the unit circle that often appears in various mathematics and physics applications.
Tips
- Confusing the coordinates at $ \frac{3\pi}{2} $ with other angles. Always refer to the specific position on the unit circle.
- Not remembering that the cosine function outputs the x-coordinate. Make sure to remember that $\cos$ gives the x-value of the point on the unit circle.
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