sin(3π/2)
Understand the Problem
The question is asking for the value of the sine function at the angle of 3π/2 radians. This can be solved using knowledge of trigonometric functions and the unit circle.
Answer
The value of $\sin\left(\frac{3\pi}{2}\right)$ is $-1$.
Answer for screen readers
The value of $\sin\left(\frac{3\pi}{2}\right)$ is $-1$.
Steps to Solve
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Identify the angle in the unit circle
We are given the angle $3\pi/2$ radians. This angle corresponds to a point on the unit circle. -
Locate the point on the unit circle
The angle $3\pi/2$ radians is located directly downward on the unit circle, which corresponds to the coordinates $(0, -1)$. -
Determine the sine value
The sine function reflects the y-coordinate of that point on the unit circle. Therefore, for the angle $3\pi/2$, the sine value is the y-coordinate of the point $(0, -1)$, which is $-1$. -
Write the final conclusion
Thus, we can conclude that the value of the sine function at the angle $3\pi/2$ radians is $-1$.
The value of $\sin\left(\frac{3\pi}{2}\right)$ is $-1$.
More Information
The angle $3\pi/2$ radians is significant because it represents a straight downward direction in the unit circle, giving a minimum value for the sine function.
Tips
- Confusing the angle with its position: It’s common to forget that $3\pi/2$ radians points downward, not upward.
- Miscalculating the sine of other angles: Students might mix up values from different angles on the unit circle; all sine values are based on the y-coordinates.
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