Find the exact value of cos 330.
Understand the Problem
The question is asking for the exact value of the cosine of the angle 330 degrees. To solve this, we can use the unit circle and trigonometric identities relating to angles and their cosine values.
Answer
$\frac{\sqrt{3}}{2}$
Answer for screen readers
The exact value of $\cos(330^\circ)$ is $\frac{\sqrt{3}}{2}$.
Steps to Solve
-
Find the reference angle
The angle of 330 degrees is in the fourth quadrant. To find the reference angle, subtract 330 degrees from 360 degrees:
$$ 360^\circ - 330^\circ = 30^\circ $$ -
Determine the cosine value
In the fourth quadrant, the cosine value is positive. The cosine of the reference angle (30 degrees) can be found using the cosine function:
$$ \cos(30^\circ) = \frac{\sqrt{3}}{2} $$ -
Conclusion for cosine at 330 degrees
Since 330 degrees is in the fourth quadrant and the cosine is positive:
$$ \cos(330^\circ) = \cos(30^\circ) = \frac{\sqrt{3}}{2} $$
The exact value of $\cos(330^\circ)$ is $\frac{\sqrt{3}}{2}$.
More Information
The angle of 330 degrees is often related to the concept of angles in the unit circle. In addition, $30^\circ$ is a standard reference angle for trigonometric values, often found in basic trigonometric tables.
Tips
- Confusing the quadrant: Remember that the cosine is positive in the fourth quadrant; it's easy to forget this and mistakenly take the negative value of the reference angle.
- Miscalculating the reference angle: Ensure to subtract the given angle from 360 degrees for angles greater than 180 degrees to find the correct reference angle in the unit circle.
