cos 30 degrees exact value
Understand the Problem
The question is asking for the exact value of cosine of 30 degrees, which is a trigonometric function. We will determine its value based on known trigonometric identities.
Answer
The exact value of $\cos(30^\circ)$ is $\frac{\sqrt{3}}{2}$.
Answer for screen readers
The exact value of $\cos(30^\circ)$ is $\frac{\sqrt{3}}{2}$.
Steps to Solve
- Identify the known value The cosine of 30 degrees can be remembered as a common trigonometric identity. It simplifies to:
$$ \cos(30^\circ) = \frac{\sqrt{3}}{2} $$
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Use trigonometric properties You can also remember that the angle of 30 degrees corresponds to the coordinates of a point on the unit circle. The point is located at ((\frac{\sqrt{3}}{2}, \frac{1}{2})). Hence, the cosine value is the x-coordinate.
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Final value interpretation Thus, the exact value of $\cos(30^\circ)$ is confirmed to be:
$$ \frac{\sqrt{3}}{2} $$
The exact value of $\cos(30^\circ)$ is $\frac{\sqrt{3}}{2}$.
More Information
The value $\frac{\sqrt{3}}{2}$ is one of the important angles in trigonometry, often used in various applications such as geometry, physics, and engineering.
Tips
- A common mistake is confusing the values for sine and cosine, so it's important to remember that $\cos(30^\circ)$ corresponds to the x-coordinate.
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