Find the Exact Value arcsec(-2)

Problem

arcsec(−2)

Solution

1. Identify the definition of the inverse secant function. The expression y=arcsec(−2) is equivalent to sec(y)=−2 where y must be in the range [0,π] and y≠π/2

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 reference angle by finding the value in the first quadrant where the cosine is positive.

cos(π/3)=1/2

4. Find the angle in the second quadrant because the cosine is negative and the range of the inverse secant is restricted to the first and second quadrants.

y=π−π/3

5. Simplify the expression to find the exact value.

y=(2*π)/3

Final Answer

arcsec(−2)=(2*π)/3

Want more problems? Check here!