find the exact value of cos 300 degrees.
cos(360-x) = cos(x)
so, same as cos 60°
To find the exact value of cos 300 degrees, we can use the trigonometric identity that relates the cosine of any angle θ with the cosine of its reference angle (360 degrees - θ). The reference angle of 300 degrees can be found by subtracting 300 from 360:
Reference angle = 360 degrees - 300 degrees = 60 degrees
Now, we can find the exact value of cos 60 degrees. A common method to determine this value is to use a triangle, specifically an equilateral triangle, because all its angles are 60 degrees. The cosine of an angle in an equilateral triangle is equal to 1/2 of the side length divided by the hypotenuse.
In an equilateral triangle, all sides are the same length. So, let's assume the side length of the triangle is 1. The hypotenuse is also 1 because it connects two vertices of the triangle. Using the cosine formula:
cos 60 degrees = (1/2) / 1 = 1/2
Therefore, the exact value of cos 300 degrees is 1/2.