Evaluate sec(420 degrees )

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. Rewrite the expression using the coterminal angle.

sec(420)=sec(60)

3. Apply the reciprocal identity for the secant function, which states that sec(θ)=1/cos(θ)

sec(60)=1/cos(60)

4. Substitute the known value for cos(60) which is 1/2

1/cos(60)=1/(1/2)

5. Simplify the fraction by multiplying by the reciprocal.

1/(1/2)=2

Final Answer

sec(420)=2

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