Question

The minimum value of the expression $\sin \alpha +\sin \beta +\sin \gamma$, where $\alpha ,\beta ,\gamma$ are the numbers satisfying $\alpha +\beta +\gamma =\pi$ is

• A. Positive
• B. Zero
• C. Negative
• D. $-3$

Answer 1

The correct option is C Negative

Taking $\alpha =\beta =-\frac{\pi }{2}$ and $\gamma =2\pi$

$\sin \alpha +\sin \beta +\sin \gamma =-2$

but min value of $\sin \alpha +\sin \beta +\sin \gamma >-3$

Therefore Minimum value of $\sin \alpha +\sin \beta +\sin \gamma$ is negative.