Find the Exact Value arcsec(2)

Problem

arcsec(2)

Solution

1. Identify the definition of the inverse secant function, where y=arcsec(x) means sec(y)=x 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. Determine the angle y in the interval [0,π] that satisfies the cosine equation.

y=π/3

4. Verify that the value π/3 falls within the restricted range of the arcsecant function.

π/3∈[0,π/2)

Final Answer

arcsec(2)=π/3

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