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sin(2*x)
A inequation with variable

The solution

sin(2*x) < cos(x)
$$\sin{\left(2 x \right)} < \cos{\left(x \right)}$$
sin(2*x) < cos(x)
Solving inequality on a graph
Rapid solution [src]
  /   /            pi\     /           3*pi    \     /pi          5*pi\\
Or|And|0 <= x, x < --|, And|x <= 2*pi, ---- < x|, And|-- < x, x < ----||
  \   \            6 /     \            2      /     \2            6  //
$$\left(0 \leq x \wedge x < \frac{\pi}{6}\right) \vee \left(x \leq 2 \pi \wedge \frac{3 \pi}{2} < x\right) \vee \left(\frac{\pi}{2} < x \wedge x < \frac{5 \pi}{6}\right)$$
((0 <= x)∧(x < pi/6))∨((x <= 2*pi)∧(3*pi/2 < x))∨((pi/2 < x)∧(x < 5*pi/6))
Rapid solution 2 [src]
    pi     pi  5*pi     3*pi       
[0, --) U (--, ----) U (----, 2*pi]
    6      2    6        2         
$$x\ in\ \left[0, \frac{\pi}{6}\right) \cup \left(\frac{\pi}{2}, \frac{5 \pi}{6}\right) \cup \left(\frac{3 \pi}{2}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, pi/6), Interval.open(pi/2, 5*pi/6), Interval.Lopen(3*pi/2, 2*pi))