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what is the inequality sign between cosx and x?
like sinx < x and x <tanx
2 Answers
- SqdancefanLv 75 years ago
cos(x) = x at about x = 0.7390851332. Below that value,
.. cos(x) > x
Above that value
.. cos(x) < x
See the source link for a graph.
Source(s): https://www.desmos.com/calculator/xzay1sbfjt - atsuoLv 65 years ago
sin(x) < x < tan(x) for 0 < x < pi/2 .
Let x = pi/2 - y .
0 < pi/2 - y < pi/2
-pi/2 < -y < 0
0 < y < pi/2
Thus
sin(pi/2 - y) < pi/2 - y < tan(pi/2 - y) for 0 < y < pi/2
cos(y) < pi/2 - y < cot(y)
Swap y and x
cos(x) < pi/2 - x < cot(x) for 0 < x < pi/2 ..... the answer
