Find the Exact Value cos(600)

Problem

cos(600)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

600−360=240

2. Determine the quadrant for 240 Since 180<240<270 the angle lies in Quadrant III.

3. Calculate the reference angle for an angle in Quadrant III using the formula (θ_ref)=θ−180

240−180=60

4. Determine the sign of the cosine function in Quadrant III. In this quadrant, cosine values are negative.

cos(600)=−cos(60)

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(60)=1/2

6. Apply the sign to find the final exact value.

cos(600)=−1/2

Final Answer

cos(600)=−1/2

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