cos of 3pi/2
Understand the Problem
The question is asking for the value of the cosine function at the angle 3Ï€/2 radians. We need to evaluate the cosine for this specific angle, which corresponds to a point on the unit circle.
Answer
0
Answer for screen readers
The final answer is 0
Steps to Solve
- Identify the angle on the unit circle
The angle $\frac{3\pi}{2}$ radians corresponds to 270 degrees, which is located on the negative y-axis of the unit circle.
- Determine the coordinates on the unit circle
The coordinates of the point at $\frac{3\pi}{2}$ radians on the unit circle are (0, -1) because it is directly below the origin at a distance of 1.
- Extract the cosine value
The cosine of an angle in the unit circle is equal to the x-coordinate of its corresponding point.
- Write the final answer
Since the x-coordinate is 0, the cosine of $\frac{3\pi}{2}$ radians is 0.
The final answer is 0
More Information
The cosine function represents the x-coordinate of a point on the unit circle. Since the point at $\frac{3\pi}{2}$ radians lies on the negative y-axis with coordinates (0, -1), the cosine value is 0.
Tips
A common mistake is not converting radians to degrees correctly or misidentifying the location on the unit circle. Always visualize where the angle lies on the unit circle to avoid this.
AI-generated content may contain errors. Please verify critical information
