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

  • Thread starter Neopets
  • Start date
  • Tags
    Mean Sin
In summary, the given information of tanθ = 1/2 > 0 and sin θ < 0 indicates that the point P = (x,y) corresponding to θ lies in quadrant 3. This is because tangent is positive in the 1st and 3rd quadrants, and sine is negative in the 3rd and 4th quadrants, so the only quadrant that satisfies both conditions is quadrant 3.
  • #1
Neopets
29
0
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
 
Physics news on Phys.org
  • #2


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.
 
  • #3


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 :)
 

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

1. Why does tanθ = 1/2?

The value of tanθ = 1/2 when θ is equal to approximately 26.57 degrees or 0.463 radians. This is because the tangent ratio is defined as the opposite side divided by the adjacent side in a right triangle, which is equal to 1/2 in this case.

2. Why is tanθ = 1/2 considered positive?

In mathematics, positive values are those that are greater than 0. Since tanθ = 1/2 is greater than 0, it is considered a positive value.

3. What does sin θ represent?

Sinθ is one of the six trigonometric functions and represents the ratio of the opposite side to the hypotenuse in a right triangle. It is also known as the "sine" of an angle.

4. Why does sin θ being positive mean that it lies in quadrant 3?

In the Cartesian coordinate system, quadrant 3 is the lower left quadrant where both the x and y coordinates are negative. Since sin θ represents the ratio of the opposite side to the hypotenuse, and both of these values are negative in quadrant 3, sin θ is positive.

5. How is quadrant 3 related to the value of tanθ = 1/2 and sin θ being positive?

When solving for tanθ = 1/2, there are two possible angles that satisfy this equation: 26.57 degrees in quadrant 1 and 206.57 degrees in quadrant 3. However, since sin θ is positive in quadrant 3, this tells us that the angle must be 206.57 degrees, which is the only angle in quadrant 3 where both tanθ = 1/2 and sin θ are positive.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
21
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
3K
  • Precalculus Mathematics Homework Help
Replies
1
Views
3K
  • Precalculus Mathematics Homework Help
Replies
10
Views
2K
  • Precalculus Mathematics Homework Help
Replies
8
Views
4K
Back
Top