Find the Exact Value arcsec( square root of 2)

Problem

arcsec(√(,2))

Solution

1. Identify the definition of the inverse secant function, where y=arcsec(√(,2)) implies sec(y)=√(,2) for y in the range [0,π/2)∪(π/2,π]

2. Rewrite the equation in terms of the cosine function using the reciprocal identity sec(y)=1/cos(y)

cos(y)=1/√(,2)

3. Rationalize the denominator to recognize the standard value from the unit circle.

cos(y)=√(,2)/2

4. Determine the angle y in the interval [0,π] that satisfies the cosine equation.

y=π/4

Final Answer

arcsec(√(,2))=π/4

Want more problems? Check here!