Which quadrant does θ lie, if sin θ > 0 and sec θ < 0
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Which quadrant does θ lie, if sin θ > 0 and sec θ < 0

[From: ] [author: ] [Date: 12-12-20] [Hit: ]
Secx is 1/cosx and cosx is negative (secxSo Quadrant 2 is the only place where both conditions are true.2) cotx is negative (cotx sinx is negative (sinx So Quadrant 4 is the only place where both conditions are true.-1. if sin > 0 then y value is positive and if sec 2.......

So what information you have is that sinθ is bigger than zero and cosθ is smaller than zero.

cosθ and sinθ correspond to the x&y values, respectively.

So.. In what quadrant is the x negative and the y positive?

That would be II

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1) Sinx is positive (sinx > 0) in Quadrant I and 2.
Secx is 1/cosx and cosx is negative (secx<0) in Quadrant 2
So Quadrant 2 is the only place where both conditions are true.

2) cotx is negative (cotx < 0) is Quadrant 2 and 4.
sinx is negative (sinx < 0) in Quadrant 3 and 4.
So Quadrant 4 is the only place where both conditions are true.

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1. if sin > 0 then y value is positive and if sec < 0 then x is negative. so, 2nd quadrant

2. if cot < 0 the is either 2nd or 4th quadrant, if sin < 0 then 3 or 4th quadrant. so its the 4th quadrant

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1) second

2) fourth

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1)

sinθ > 0 in Q1 and Q2
secθ < 0 ----> cosθ < 0 in Q2 or Q3
Q2

2)

cotθ < 0 in Q2 and Q4
sinθ < = in Q3 and Q4
Q4
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