Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary.
-sin (arctan 2)
A)Undefined
B)0.8944
C)-0.8172
D)0

Question

Quizplus · Accepted Answer

The value of sin(arctan(2)) can be found by considering a right triangle where the opposite side to the angle is 2 and the adjacent side is 1 (from the definition of tan(theta) = opposite/adjacent). Using the Pythagorean theorem, the hypotenuse is sqrt(1^2 + 2^2) = sqrt(5). Therefore, sin(arctan(2)) = opposite/hypotenuse = 2/sqrt(5), which when simplified and rounded to four decimal places is approximately 0.8944.

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