Why does tanθ = 1/2 > 0 and sin θ mean that it lies in quadrant 3

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The discussion clarifies that the conditions tanθ = 1/2 > 0 and sin θ < 0 indicate that the angle θ lies in the third quadrant. Tangent is positive in the first and third quadrants, while sine is negative in the third and fourth quadrants. The overlap of these conditions confirms that the only quadrant satisfying both is the third. Participants express gratitude for the explanation, indicating it helped their understanding of the problem. This insight aids in solving similar trigonometric problems effectively.
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why does tanθ = 1/2 > 0 and sin θ" mean that it lies in quadrant 3

Homework Statement


Given one value of a trigonometric function, and the sign of another, find the remaining ones
Given that tanθ = 1/2 > 0 and sin θ < 0 , the point P = (x,y) that corresponds to θ , lies in quadrant 3

Homework Equations


The Attempt at a Solution


attempted to draw a picture, using a circle with the four quadrants as is the next step for the problem, but need to know,
need to ask a question about just that first part of what's in the book for this problem, so the new question about the original problem in the book is, how does that information indicate that the point that corresponds to θ lies in quadrant 3 ? (More specifically, how does "Given that tanθ = 1/2 > 0 and sin θ < 0" mean that it lies in quadrant 3, what indicates that?
Can anyone go into more detail about why this is? Just want a real person because the book puts it in a fashion that is not human so to speak
 
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Now that you added that sin θ<0, I understand the problem!

Tangent is positive in the 1st and 3rd quadrants. Sine is negative in the 3rd and 4th quadrants. Choose the quadrant that overlaps.
 


mharten1 said:
Now that you added that sin θ<0, I understand the problem!

Tangent is positive in the 1st and 3rd quadrants. Sine is negative in the 3rd and 4th quadrants. Choose the quadrant that overlaps.

Thanks seems to help, will try some problems and let you know :) thank you so much by the way you just made my day :)
 
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