Simplify sec(45)

Problem

sec(45^∘)

Solution

1. Identify the definition of the secant function in terms of the cosine function.

sec(θ)=1/cos(θ)

2. Substitute the given angle of 45^∘ into the identity.

sec(45^∘)=1/cos(45^∘)

3. Recall the exact value of cos(45^∘) from the unit circle.

cos(45^∘)=√(,2)/2

4. Substitute the value of the cosine into the expression and simplify the fraction.

sec(45^∘)=1/√(,2)/2

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

sec(45^∘)=2/√(,2)

sec(45^∘)=(2√(,2))/2

sec(45^∘)=√(,2)

Final Answer

sec(45^∘)=√(,2)

Want more problems? Check here!