MathDB

0, 1, 2, 3, 0, ...

Source: 2019 AIME ii #10

March 22, 2019

AMCAIMEAIME II2019 AIME II2019 AMC

Problem Statement

There is a unique angle

\theta

between

0^{\circ}

and

90^{\circ}

such that for nonnegative integers

n

, the value of

\tan{\left(2^{n}\theta\right)}

is positive when

n

is a multiple of

3

, and negative otherwise. The degree measure of

\theta

is

\tfrac{p}{q}

, where

p

and

q

are relatively prime integers. Find

p+q

.

Back to Problems View on AoPS