Find the Exact Value sec(45)

Problem

sec(45)

Solution

1. Identify the relationship between the secant function and the cosine function using the reciprocal identity.

sec(45)=1/cos(45)

2. Determine the exact value of cos(45) using the unit circle or a special right triangle (45−45−90.

cos(45)=√(,2)/2

3. Substitute the value of the cosine function back into the reciprocal identity.

sec(45)=1/√(,2)/2

4. Simplify the complex fraction by multiplying by the reciprocal of the denominator.

sec(45)=2/√(,2)

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

sec(45)=(2√(,2))/2

6. Reduce the fraction to its simplest form.

sec(45)=√(,2)

Final Answer

sec(45)=√(,2)

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