Range of Trigonometric Ratios from 0 to 90 Degrees
If α ,β ,γ ...
Question
If α,β,γ are real numbers satisfying α+β+γ=π. The minimum value of the given expression sinα+sinβ+sinγ is
A
Zero
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B
−3
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C
Positive
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D
Negative
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Solution
The correct option is C Positive Since, sinα+sinβ+sinγ>sin(α+β+γ) Given, α+β+γ=π ⇒sinα+sinβ+sinγ>sinπ=0 Hence, the minimum value of sinα+sinβ+sinγ is always positive.