find the exact value of cos 330
Using the unit circle, we can see that 330 degrees starts in the fourth quadrant and rotates clockwise. To find the cosine of 330 degrees, we can find the reference angle by subtracting 360 degrees from 330 degrees, giving us 330 - 360 = -30 degrees.
Since cosine is an even function, we know that cos(-30) is the same as cos(30). Looking at the unit circle, we see that the cos value for 30 degrees is √3/2.
Therefore, cos 330 = cos(-30) = cos 30 = √3/2.
The exact value of cos 330 is √3/2.
To find the exact value of cos 330 degrees, we can use the trigonometric identity:
cos (360 degrees - x) = cos x
Using this identity, we can rewrite cos 330 as:
cos 330 degrees = cos (360 degrees - 30 degrees)
Now, we know that cos 30 degrees = √3 / 2 (which can be derived from the 30-60-90 degrees triangle). Therefore, we have:
cos 330 degrees = cos (360 degrees - 30 degrees) = cos 30 degrees = √3 / 2
So, the exact value of cos 330 degrees is √3 / 2.