1989 AMC 12 Problem 28
Attempt Problem 28 of the 1989 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Find the sum of the roots of that are between and radians.
Answer: D
Small hint:
Let the two positive roots in be and
Big hint:
Use to relate then include the period of tangent
Solution:
The two roots of are positive and satisfy Therefore their acute arctangents add to Each tangent value occurs twice between and with the second occurrence shifted by The sum of all four roots is
Thus the correct answer is D.
Problem 28 in other years
- 1950 AMC 12
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