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MATH / For 135^(∘)<x<180^(∘), points P=(cos x, cos^2 x), Q=(cot x, cot^2 x), R=(sin x, sin^2 x) and S=(tanx,tan²x) are the vertices of a trapezoid. What is sin2x?

Problem

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problem

For 135∘<x<180∘135^\circ < x < 180^\circ, points $P=(\cos x, \cos^2 x), Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x)$ and S=(tanx,tan2x)S =(\tan x, \tan^2 x) are the vertices of a trapezoid. What is sin2x\sin 2x?
Plain-text mathematical notation (without MathML)
For 135^(∘)<x<180^(∘), points $P=(\cos x, \cos^2 x), Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x)$ and S=(tanx,tan²x) are the vertices of a trapezoid. What is sin2x?
Original LaTeX notation
For $135^\circ < x < 180^\circ$, points $P=(\cos x, \cos^2 x), Q=(\cot x, \cot^2 x), R=(\sin x, \sin^2 x)$ and $S =(\tan x, \tan^2 x)$ are the vertices of a trapezoid. What is $\sin 2x$?

level

Level 5

type

Precalculus

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Source and history

task_id
4702c44f-6826-5f69-a510-8f183fc70e97
task_key
precalculus--test--4702c44f-6826-5f69-a510-8f183fc70e97
task_revision_id
1
config / split
precalculus / test

Official source

initial import