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Omni-MATH / Determine the number of angles θ between 0 and 2π, other than integer multiples of π/2, such that the quantities sinθ,cosθ, and tanθ form a geometric sequence in some order.

Problem

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problem

Determine the number of angles θ\theta between 0 and 2π2 \pi, other than integer multiples of π/2\pi / 2, such that the quantities sinθ,cosθ\sin \theta, \cos \theta, and tanθ\tan \theta form a geometric sequence in some order.
Plain-text mathematical notation (without MathML)
Determine the number of angles θ between 0 and 2π, other than integer multiples of π/2, such that the quantities sinθ,cosθ, and tanθ form a geometric sequence in some order.
Original LaTeX notation
Determine the number of angles $\theta$ between 0 and $2 \pi$, other than integer multiples of $\pi / 2$, such that the quantities $\sin \theta, \cos \theta$, and $\tan \theta$ form a geometric sequence in some order.

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Source and history

task_id
9d8469b6-75df-52ae-a538-3ce6c40dd9b5
task_key
test--9d8469b6-75df-52ae-a538-3ce6c40dd9b5
task_revision_id
1
config / split
/ test

Official source

initial import