Use a calculator to find the approximate value of the composition. Round answers to four decimal places. The expression
may be undefined.
-sec (arctan (4.839))
A) 0.2024
B) 4.9412
C) 0.4999
D) 1.0000

Question

Quizplus · Accepted Answer

To solve this, we first understand what the composition of functions sec(arctan(x)) means. The arctan function gives us an angle whose tangent is x. In this case, x = 4.839. Then, taking the secant of this angle gives us the reciprocal of the cosine of the angle. Since the tangent of an angle in a right triangle is the opposite side over the adjacent side, if we consider a triangle where the opposite side is 4.839 and the adjacent side is 1 (to make the math simpler), the hypotenuse (using Pythagoras' theorem) would be sqrt(1^2 + 4.839^2) = sqrt(1 + 23.415521) = sqrt(24.415521). The secant is the reciprocal of the cosine, which is the hypotenuse over the adjacent side, so in this case, it would be sqrt(24.415521)/1. Calculating this gives an approximate value of 4.9412, which matches option B.

Use a Calculator to Find the Approximate Value of the Composition