Solving x/2 in 3rd Quadrant: Cosx=-7/9

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In summary, the conversation is about finding the values of cos(x/2) and sin(x/2) when given cosx = -7/9 in the third quadrant. The formula used is sin^2x=1-cos2x/2 and the correct method is to rewrite the equality as ## \sin^2\frac{x}{2} = \frac{1 - \cos x}{2} ## and ensure the correct sign. There may be one small step to simplify the answer.
  • #1
zaddyzad
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Homework Statement



We have cosx = -7/9 in the third quadrant, and my question is how to find cos(x/2) and sin(x/2).

I've tried using the sin^2x=1-cos2x/2 formula and its adjacent cosine formula. Is this the correct formula I should be using to get the answer for this question?
 
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  • #2
Yes. You say you tried, what happened? Try rewriting the equality as ## \sin^2\frac{x}{2} = \frac{1 - \cos x}{2} ##; make sure your answer has the correct sign.
 
  • #3
MrAnchovy said:
Yes. You say you tried, what happened? Try rewriting the equality as ## \sin^2\frac{x}{2} = \frac{1 - \cos x}{2} ##; make sure your answer has the correct sign.

It worked for the sin(x/2), but when I tried for the cos(x/2)... I got 1+(-7/9) / 2 which becomes sqrt(2/18). Is this what you get ??
 
  • #4
You can simplify [itex]\sqrt{\frac{2}{18}}[/itex], you know. :tongue: Also, there's one little thing you're forgetting. MrAnchovy mentions it in his post.
 

1. What does it mean to solve x/2 in the 3rd quadrant?

Solving x/2 in the 3rd quadrant means finding the value of x when the angle is in the 3rd quadrant and divided by 2. This involves using the trigonometric functions of cosine and tangent to determine the value of x.

2. How do I know if I need to solve x/2 in the 3rd quadrant?

If the given equation is in the form of cosine and the value being solved for is divided by 2, then it is likely that the solution will be in the 3rd quadrant. It is important to pay attention to the given equation and determine the appropriate quadrant based on the trigonometric function and value being solved for.

3. Can I use a calculator to solve x/2 in the 3rd quadrant?

Yes, you can use a calculator to solve x/2 in the 3rd quadrant. Most scientific calculators have functions for cosine and tangent which can be used to find the value of x. However, it is important to make sure the calculator is set to the correct mode (degrees or radians) and to use parentheses when necessary.

4. What is the process for solving x/2 in the 3rd quadrant?

The process for solving x/2 in the 3rd quadrant involves using the given equation and the trigonometric functions of cosine and tangent. First, determine the appropriate quadrant based on the given equation. Then, use the inverse cosine function to find the angle measure. Finally, use the tangent function to find the value of x by multiplying the angle measure by 2.

5. Are there any special considerations when solving x/2 in the 3rd quadrant?

When solving x/2 in the 3rd quadrant, it is important to remember that the cosine function is negative in the 3rd quadrant. This means that the angle measure found using the inverse cosine function will be negative. Additionally, when using a calculator, make sure to use parentheses and double check the mode setting to ensure an accurate solution.

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