Evaluate arcsec(2)

Problem

arcsec(2)

Solution

1. Identify the definition of the inverse secant function. The expression y=arcsec(2) is equivalent to finding an angle y such that sec(y)=2 within the restricted range [0,π/2)∪(π/2,π]

2. Convert the secant function to the cosine function using the reciprocal identity sec(y)=1/cos(y)

3. Set up the equation for cosine.

cos(y)=1/2

4. Determine the angle y in the first quadrant that satisfies the equation. From the unit circle, the cosine of π/3 is 1/2

y=π/3

Final Answer

arcsec(2)=π/3

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