Find the Exact Value sec(420)

Problem

sec(420)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the first rotation.

420−360=60

2. Identify the reciprocal identity for the secant function, which relates it to the cosine function.

sec(60)=1/cos(60)

3. Determine the cosine value for the reference angle of 60 using the unit circle or special right triangles.

cos(60)=1/2

4. Substitute and simplify the expression to find the final numerical value.

sec(60)=1/(1/2)=2

Final Answer

sec(420)=2

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