Find the Exact Value cos(420)

Problem

cos(420)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard range of 0 to 360

420−360=60

2. Identify the quadrant for the angle 60 which is in the first quadrant where all trigonometric functions are positive.

cos(420)=cos(60)

3. Determine the exact value using the unit circle or special right triangles (30−60−90.

cos(60)=1/2

Final Answer

cos(420)=1/2

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