What is the exact value of sin(pi/6)?
Understand the Problem
The question is asking for the exact value of the sine function evaluated at the angle π/6 radians.
Answer
$\frac{1}{2}$
Answer for screen readers
The exact value of the sine function at the angle $\frac{\pi}{6}$ radians is $\frac{1}{2}$.
Steps to Solve
-
Identify the angle in degrees
The angle given is in radians, specifically $\frac{\pi}{6}$. To understand it better, we can convert this angle into degrees:
$$ \frac{\pi}{6} \times \frac{180}{\pi} = 30^\circ $$ -
Recall the sine value for common angles
The sine function has known values for certain angles. For $30^\circ$, we have:
$$ \sin\left(30^\circ\right) = \frac{1}{2} $$ -
Conclusion
Thus, the exact value of the sine function evaluated at the angle $\frac{\pi}{6}$ radians is:
$$ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} $$
The exact value of the sine function at the angle $\frac{\pi}{6}$ radians is $\frac{1}{2}$.
More Information
The sine of $30^\circ$ (or $\frac{\pi}{6}$ radians) being $\frac{1}{2}$ is a fundamental value in trigonometry and is often used in various applications, including physics and engineering.
Tips
- Confusing radians and degrees can lead to incorrect values; always ensure to be clear on which unit you are working with.
