Find the Exact Value cos(405)

Problem

cos(405)

Solution

1. Identify the angle as being greater than 360 which means it completes more than one full rotation around the unit circle.

2. Find the coterminal angle by subtracting 360 from 405 to bring the angle within the standard range of 0 to 360

θ=405−360

θ=45

3. Apply the property that trigonometric functions of coterminal angles are equal.

cos(405)=cos(45)

4. Evaluate the cosine of 45 using the unit circle or special right triangles.

cos(45)=√(,2)/2

Final Answer

cos(405)=√(,2)/2

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