cos(pi/3) in fraction
Understand the Problem
The question is asking for the cosine of the angle pi/3 radians expressed as a fraction. This is a trigonometry question that requires knowledge of the unit circle and trigonometric values for standard angles.
Answer
The cosine of $\frac{\pi}{3}$ is $\frac{1}{2}$.
Answer for screen readers
The cosine of the angle $\frac{\pi}{3}$ radians is $\frac{1}{2}$.
Steps to Solve
-
Identify the Angle
The angle we are working with is $\frac{\pi}{3}$ radians. -
Reference the Unit Circle
On the unit circle, the angle $\frac{\pi}{3}$ corresponds to 60 degrees. -
Find the Cosine Value
The cosine of 60 degrees (or $\frac{\pi}{3}$ radians) is known from trigonometric values. The value is $\frac{1}{2}$. -
Express as a Fraction
Since we want the answer in fraction form, we write the cosine value as $\frac{1}{2}$.
The cosine of the angle $\frac{\pi}{3}$ radians is $\frac{1}{2}$.
More Information
The cosine of an angle in the unit circle represents the x-coordinate of the corresponding point. The angle $\frac{\pi}{3}$ radians is a standard angle, easy to remember, and frequently used in trigonometry.
Tips
- Confusing the angles: Remember that $\frac{\pi}{3}$ radians is equal to 60 degrees, not 30 or 45 degrees.
- Forgetting that cosine represents the x-coordinate; it's a common point of confusion when first learning trigonometry.
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