Find the Exact Value cos(390)

Problem

cos(390^∘)

Solution

1. Identify the angle as being greater than 360^∘ and find its coterminal equivalent within the range [0^∘,360^∘)

2. Subtract 360^∘ from the given angle to find the coterminal angle.

θ=390^∘−360^∘

θ=30^∘

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

cos(390^∘)=cos(30^∘)

4. Evaluate the cosine of 30^∘ using the unit circle or special right triangles.

cos(30^∘)=√(,3)/2

Final Answer

cos(390^∘)=√(,3)/2

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