Find the Exact Value sec(arctan(9/10))

Problem

sec(arctan(9/10))

Solution

1. Identify the inner function as an angle θ such that θ=arctan(9/10)

2. Relate the tangent function to the sides of a right triangle, where tan(θ)=opposite/adjacent=9/10

3. Determine the hypotenuse r using the Pythagorean theorem r=√(,a2+b2)

r=√(,10+9)

r=√(,100+81)

r=√(,181)

4. Apply the definition of the secant function, which is sec(θ)=hypotenuse/adjacent

sec(θ)=√(,181)/10

Final Answer

sec(arctan(9/10))=√(,181)/10

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