Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
-sec (arctan 4.839)
A)4.9412
B)0.5
C)1
D)0.2024

Question

Quizplus · Accepted Answer

To solve sec(arctan(4.839)), we first find the angle whose tangent is 4.839. Then, we find the secant of that angle. Since secant is the reciprocal of cosine, and cosine is adjacent over hypotenuse in a right triangle, we can construct a triangle where the opposite side (to the angle found by arctan) is 4.839 and the adjacent side is 1 (for simplicity). The hypotenuse is then sqrt(1^2 + 4.839^2) = sqrt(24.4152). Therefore, sec(arctan(4.839)) = 1/cos(arctan(4.839)) = hypotenuse/adjacent = sqrt(24.4152)/1 ≈ 4.9412.

Use a Calculator to Find the Value