Question
Download Solution PDFIf \(\sin \theta = - \frac{1} {2}\) and \(\tan \theta = \frac{1} {{\sqrt 3 }}\), then in which quadrant does θ lie?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
1) In First quadrant all trigonometric identities are positive.
2) In second quadrant sin and cosec are positive.
3) In Third quadrant tan and cot are positive
4) In Fourth quadrant cos and sec are positive.
Explanation:
Given sinθ = -1/2 and tanθ = 1/√3
sinθ is negative this is possible only when
θ lies in 3rd quadrant or in 4th quadrant
and tanθ is positive, this is possible only when
θ lies in 1st quadrant or in 3rd quadrant
From the above two statements, we can say that if θ lies in 3rd quadrant then sin θ is negative and tan θ is positive.
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