Find the Exact Value arcsec(-1)

Problem

arcsec(−1)

Solution

1. Identify the definition of the inverse secant function. The expression y=arcsec(x) means sec(y)=x where y is restricted to the range [0,π] and y≠π/2

2. Set up the equation based on the given value.

sec(y)=−1

3. Relate the secant function to the cosine function using the identity sec(y)=1/cos(y)

1/cos(y)=−1

4. Solve for cos(y) by taking the reciprocal of both sides.

cos(y)=−1

5. Determine the angle y within the interval [0,π] that satisfies the equation. On the unit circle, the cosine of an angle is −1 at π radians.

y=π

Final Answer

arcsec(−1)=π

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