Question

What is the minimum value of \(\rm 2\sin \left(A-\dfrac{\pi}{3}\right)\) where A ∈ R ?
1. -2
2. -1
3. 0
4. 2

Answer 1

Correct Answer - Option 1 : -2

Concept:

The range of sine function is [-1,1] i.e \(\rm \Rightarrow -1\leq sin(x) \leq 1\)

 

Calculation:

We can write, \(\rm sin(A - \frac{\pi}{3}) \in [-1,1]\)

\(\rm \Rightarrow -1\leq sin(A - \frac{\pi}{3}) \leq 1\)

\(\rm \Rightarrow -2\leq 2sin(A - \frac{\pi}{3}) \leq 2\)

So, from the relation, we can conclude that the minimum value of 2sin(A - \(\rm \frac{\pi}{3}\)) is -2.