Evaluate sec(405 degrees )

Problem

sec(405)

Solution

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

405−360=45

2. Rewrite the expression using the coterminal angle.

sec(405)=sec(45)

3. Apply the reciprocal identity for the secant function, which is the reciprocal of the cosine function.

sec(45)=1/cos(45)

4. Substitute the known value for cos(45) which is √(,2)/2

sec(45)=1/√(,2)/2

5. Simplify the fraction by multiplying by the reciprocal.

1/√(,2)/2=2/√(,2)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

(2√(,2))/2=√(,2)

Final Answer

sec(405)=√(,2)

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