Emily is preparing for an upcoming event where she will be using props designed by someone else. She needs to find the exact calculations for an angle that has been given in radians so that she can ensure that the props are set up correctly. The angle in question is π3π3 radians. Emily specifically needs to know the exact value of the sine of this angle.    

Find the exact value of sin(π/3). 

To find the exact value of \( \sin\left(\frac{\pi}{3}\right) \), we can refer to the unit circle or use trigonometric identities.

The angle \( \frac{\pi}{3} \) radians corresponds to 60° in degrees.

The sine of \( 60^\circ \) or \( \frac{\pi}{3} \) radians is a well-known value:

\[
\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}
\]

Thus, the exact value of \( \sin\left(\frac{\pi}{3}\right) \) is \( \frac{\sqrt{3}}{2} \).

Would you like more details on how this result is derived or have any questions?

---

Here are some related questions:
1. What is the cosine of \( \frac{\pi}{3} \)?
2. How can you derive trigonometric values for standard angles?
3. What is the unit circle, and how is it used in trigonometry?
4. How does \( \sin\left(\frac{\pi}{3}\right) \) compare with \( \sin\left(\frac{\pi}{6}\right) \)?
5. What is the value of \( \tan\left(\frac{\pi}{3}\right) \)?

**Tip:** Knowing the sine, cosine, and tangent values of key angles (like \( 30^\circ \), \( 45^\circ \), and \( 60^\circ \)) helps in solving many trigonometric problems quickly!

Emily is preparing for an upcoming event where she will be using props designed by someone else. She needs to find the exact calculations for an angle that has been given in radians so that she can ensure that the props are set up correctly. The angle in question is π/3 radians. Emily specifically needs to know the exact value of the sine of this angle.

Find the exact value of sin(π/3) with a detailed explanation using trigonometric principles. Learn about radians, the unit circle, and how to convert angles between radians and degrees. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation