Trigonometric inequalities (simplest, using the unit circle)

Why the unit circle

Trigonometric inequality — find all $x$ such that, e.g., $\sin x\gt m$ or $\cos x\geqslant m$ (and analogues with $\tan x,\ \cot x$ ). On the unit circle, $\sin x$ and $\cos x$ are the y- and x-coordinates of the arc endpoint of length $|x|$ from $(1;0)$ . To read $\sin x\gt m$ : draw the horizontal line $y=m$ and take arcs where the point on the circle lies above that line (strictly above if the sign is $\gt$ ; on the boundary treat $\geqslant$ separately). For $\cos x$ — symmetrically with the vertical line $x=m$ (where $m\in[-1;1]$ ).

First solve on one turn $[0;2\pi)$ (or the standard interval for $\tan$ ), then add $+2\pi k$ or $+\pi k$

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