Find the Exact Value sec(360)

Problem

sec(360^∘)

Solution

1. Identify the angle and the trigonometric function. The angle is 360^∘ which is coterminal with 0^∘ on the unit circle.

2. Apply the definition of the secant function in terms of cosine.

sec(θ)=1/cos(θ)

3. Determine the value of cos(360^∘) On the unit circle, the point corresponding to 360^∘ is (1,0)

cos(360^∘)=1

4. Substitute the value of the cosine into the secant formula.

sec(360^∘)=1/1

5. Simplify the fraction to find the final result.

sec(360^∘)=1

Final Answer

sec(360^∘)=1

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