First slide

Properties of ITF

Question

If $\cos^{- 1} (\frac{n}{2 π}) > \frac{2 π}{3}$ then the minimum and the maximum values of integer n are respectively.

Moderate

A

– 6 and – 4
B

4 and 6
C

– 6 and – 3
D

none of these

Solution

We have,
$\begin{array}{l} \frac{2 π}{3} < \cos^{- 1} (\frac{n}{2 π}) < π \Rightarrow \cos \frac{2 π}{3} > \frac{n}{2 π} > \cos π \\ \Rightarrow - 1 < \frac{n}{2 π} < - \frac{1}{2} \Rightarrow - 2 π < n < - π \\ \Rightarrow - 6 < n < - 4 \end{array}$

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