Find the Exact Value sec(315)

Problem

sec(315^∘)

Solution

1. Identify the reference angle by finding the difference between 315^∘ and 360^∘ since the angle is in the fourth quadrant.

(θ_ref)=360^∘−315^∘=45^∘

2. Determine the sign of the secant function in the fourth quadrant. Since sec(θ)=1/cos(θ) and cosine is positive in the fourth quadrant, the result will be positive.

sec(315^∘)=sec(45^∘)

3. Apply the reciprocal identity to relate secant to cosine.

sec(45^∘)=1/cos(45^∘)

4. Substitute the known exact value for cos(45^∘)=√(,2)/2

sec(315^∘)=1/√(,2)/2

5. Simplify the fraction by multiplying by the reciprocal.

sec(315^∘)=2/√(,2)

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

sec(315^∘)=(2√(,2))/2=√(,2)

Final Answer

sec(315^∘)=√(,2)

Want more problems? Check here!