What is the exact value of sin(pi/3)?
Understand the Problem
The question is asking for the exact value of the sine function at the angle pi/3 radians. This is a basic trigonometric problem that requires knowledge of the unit circle or trigonometric identities.
Answer
The exact value of the sine function at the angle $\frac{\pi}{3}$ radians is $\frac{\sqrt{3}}{2}$.
Answer for screen readers
The exact value of the sine function at the angle $\frac{\pi}{3}$ radians is $\frac{\sqrt{3}}{2}$.
Steps to Solve
- Identify the angle in degrees Convert the angle from radians to degrees for better understanding. Since $1 \text{ radian} = \frac{180}{\pi} \text{ degrees}$, we can calculate the degrees as follows:
$$ \frac{\pi}{3} \text{ radians} = \frac{\pi}{3} \times \frac{180}{\pi} = 60 \text{ degrees} $$
- Use the unit circle or trigonometric values We can now find the sine of $60$ degrees using trigonometric values. From the unit circle, we know:
$$ \sin(60^\circ) = \frac{\sqrt{3}}{2} $$
- State the exact value Therefore, the exact value of the sine function at the angle $\frac{\pi}{3}$ radians is:
$$ \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} $$
The exact value of the sine function at the angle $\frac{\pi}{3}$ radians is $\frac{\sqrt{3}}{2}$.
More Information
The sine function at $\frac{\pi}{3}$ radians (or $60$ degrees) represents a commonly known value in trigonometry. It is often used in various applications, including physics, engineering, and geometry. Furthermore, the sine function is periodic, meaning it repeats values at regular intervals.
Tips
- Misremembering the values of sine at key angles such as $30^\circ$, $45^\circ$, and $60^\circ$. To avoid this, it's helpful to memorize the sine values of these key angles.
- Confusing radians and degrees. Always ensure you are using the correct angle measurement for the problem.
AI-generated content may contain errors. Please verify critical information
