Determine the quadrant in which theta lies-1- sin theta gt-0 - sec theta lt-0

Dear student 1) #160;sin #952; #62;0In #160;I #160;and #160;II #160;quadrant #160;sine #160;is #160;positive2) #160;sec #952; #60;0In ...

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Sign of Trigonometric Ratios in Different Quadrants

determine the...

Question

determine the quadrant in which theta lies.
1) sin theta>0 , sec theta<0

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θ

sin θ > 0, sec θ < 0

sec θ + tan θ = \frac{2}{3}

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sin θ sec θ = - 1

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sin \frac{θ}{2} + cos \frac{θ}{2} = - \frac{1}{2}

sin 2 θ

\sqrt{\frac{\sec θ - 1}{\sec θ + 1}} + \sqrt{\frac{\sec θ + 1}{\sec θ - 1}} = 2 cosec θ

\sqrt{\frac{1 + \sin θ}{1 - \sin θ}} + \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} = 2 \sec θ

\sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

\frac{\sec θ - 1}{\sec θ + 1} = {(\frac{\sin θ}{1 + \cos θ})}^{2}

\frac{\sin θ + 1 - \cos θ}{\cos θ - 1 + \sin θ} = \frac{1 + \sin θ}{\cos θ}

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