Answer:
1/2
Explanation:
Exact value means put the calculator away and go to an x/y coordinate plane. Set the angle up in standard position with the initial ray on the positive x-axis and the terminal ray will move counterclockwise around until is sweeps out a 300 degree angle. That angle will be in the fourth quadrant, 60 degrees BELOW the x-axis you started on. But we are not using the negative value, which is measured clockwise. From the negative y axis that is the 270 degree line, we add 30 to that 270 and get the 300 degree angle we want. Angles are always measured from the terminal ray to whichever x-axis its closest to. From the terminal ray to the x-axis forms a 60 degree angle. That means that the reference angle is 60. The side across from a 60 degree angle in a 30-60-90 right triangle is square root of 3, but our side is in the negative y's so it is . Along the x axis is the side across from the 30 degree angle which is a +1. The hypotenuse is 2. These values are from the Pythagorean triple for a 30-60-90 right triangle and should be familiar at this point. The cos identity is the side adjacent to the reference angle over the hypotenuse so our exact value for cos 300 is 1/2.
