Solving a Trig Question in 3rd Quadrant

  • Thread starter zaddyzad
  • Start date
  • Tags
    Trig
In summary, the conversation discusses solving for sin(x/2) when given cosx = -5/6 in the third quadrant. The speaker shares their process of using the trigonometric identity sin^2(x/2) = 1-cos(x)/2 to arrive at sin^2(x/2) = 11/12. They question why the positive value is chosen instead of the expected negative value based on the location of x/2 in the third quadrant. The discussion also mentions the range of angles in the third quadrant and the importance of careful notation.
  • #1
zaddyzad
149
0

Homework Statement



We have cosx = -5/6 in the third quadrant, and I solved for sin(x/2).

I did sin^2(x/2) = 1-cos(x)/2 --> I get to sin^2(x/2)= 11/12, and here's my question.

When rooting I should choose the negative value because sine is negative in the third quadrant right? But in my webwork, the answer is the positive one. Can anyone explain to me why this is?
 
Physics news on Phys.org
  • #2
Your basis for the answer being negative is that sin(x) < 0 in the third quadrant, but what does this tell you about the sign of sin(x/2)?

It may help to think angles in the third quadrant are in the range 180 < x < 270.
 
Last edited:
  • #3
is that the only basis of choosing the right sign? it being 90<x<135 ?
 
  • #4
zaddyzad said:
is that the only basis of choosing the right sign? it being 90<x<135 ?

Yes, x/2 is located in the second quadrant. And the sign of sine is positive in quadrant II.

Also, you should be careful with notation. We have 90 < x/2 < 135, not 90 < x < 135.
 

1. How do I determine the reference angle in the 3rd quadrant?

In the 3rd quadrant, the reference angle is the angle formed between the terminal side of the given angle and the x-axis. To find it, subtract the given angle from 180 degrees.

2. What is the sign of the trigonometric ratios in the 3rd quadrant?

In the 3rd quadrant, only the sine and cosecant ratios are positive, while the cosine, tangent, secant, and cotangent ratios are all negative.

3. Can I use the Pythagorean identities in the 3rd quadrant?

Yes, the Pythagorean identities (sin^2θ + cos^2θ = 1 and tan^2θ + 1 = sec^2θ) can be used in any quadrant, including the 3rd quadrant.

4. How do I solve a trig equation in the 3rd quadrant?

To solve a trig equation in the 3rd quadrant, first determine the reference angle and then use the appropriate trigonometric ratio based on the quadrant to find the value of the angle. Remember to consider the negative sign for certain ratios in the 3rd quadrant.

5. Can the unit circle be used to solve trig questions in the 3rd quadrant?

Yes, the unit circle can be used to solve trig questions in any quadrant, including the 3rd quadrant. It can help determine the coordinates and signs of the trigonometric ratios for a given angle in the 3rd quadrant.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
15
Views
496
  • General Math
Replies
16
Views
1K
  • Precalculus Mathematics Homework Help
Replies
21
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
10
Views
985
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
905
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Replies
2
Views
136
Back
Top