Simplify cos(300)

Problem

cos(300)

Solution

1. Identify the reference angle by finding the difference between 300 and the nearest multiple of 180 or 360

2. Calculate the reference angle using 360−300=60

3. Determine the quadrant of the original angle. Since 270<300<360 the angle lies in Quadrant IV.

4. Apply the sign rule for the cosine function. In Quadrant IV, the cosine of an angle is positive.

5. Evaluate the trigonometric function using the reference angle: cos(300)=cos(60)

6. Substitute the known value for cos(60) which is 1/2

Final Answer

cos(300)=1/2

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