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OlympiadBench / 2332 / Determine all pairs of angles (x,y) with 0^(∘)≤x<180^(∘) and…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Determine all pairs of angles

(x, y)

with

0^{\circ} \leq x<180^{\circ}

and

0^{\circ} \leq y<180^{\circ}

that satisfy the following system of equations:

$$
\begin{aligned}
\log _{2}(\sin x \cos y) & =-\frac{3}{2} \\
\log _{2}\left(\frac{\sin x}{\cos y}\right) & =\frac{1}{2}
\end{aligned}
$$

Plain-text mathematical notation (without MathML)

Determine all pairs of angles (x,y) with 0^(∘)≤x<180^(∘) and 0^(∘)≤y<180^(∘) that satisfy the following system of equations:

$$
\begin{aligned}
\log _{2}(\sin x \cos y) & =-\frac{3}{2} \\
\log _{2}\left(\frac{\sin x}{\cos y}\right) & =\frac{1}{2}
\end{aligned}
$$

Original LaTeX notation

Determine all pairs of angles $(x, y)$ with $0^{\circ} \leq x<180^{\circ}$ and $0^{\circ} \leq y<180^{\circ}$ that satisfy the following system of equations:

$$
\begin{aligned}
\log _{2}(\sin x \cos y) & =-\frac{3}{2} \\
\log _{2}\left(\frac{\sin x}{\cos y}\right) & =\frac{1}{2}
\end{aligned}
$$

answer type

Tuple

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2332
task_id: ba5ab108-e71b-53ab-a7ca-e88f8a5d2ebd
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2332
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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