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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