How do i find the value of cos(theta)

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In summary, to find the value of cos(theta) with an uncertainty of 5°, you can use the Taylor expansion cos (\theta \pm \delta \theta) \approx cos(\theta) \pm (\delta \theta) ~sin(\theta) where (\delta \theta) must be in radians. This may result in an uncertainty larger than the actual value of cos(theta).
  • #1
gunblaze
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How do i find the value of cos(theta) if theta was given as 75(+/-)5?

Ans:____(+/-)_____.

How do i even start with this? How do i find the uncertainty of cos (theta)? Do i use the uncertainty of theta or the fractional uncertainty? Or do i just find cos 80, cos 75 and cos 70 and then find the uncertainty by deducing it from the found values/.?

Any help will truly be appreciated. Thanks.
 
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  • #2
gunblaze said:
How do i find the value of cos(theta) if theta was given as 75(+/-)5?

Ans:____(+/-)_____.

How do i even start with this? How do i find the uncertainty of cos (theta)? Do i use the uncertainty of theta or the fractional uncertainty? Or do i just find cos 80, cos 75 and cos 70 and then find the uncertainty by deducing it from the found values/.?

Any help will truly be appreciated. Thanks.
You use a Taylor expansion.
The result is that
[tex]
cos (\theta \pm \delta \theta) \approx cos(\theta) \pm (\delta \theta) ~sin(\theta)[/tex]
where you must use [itex] \delta \theta [/itex] in radians .

Hope this helps.

Patrick
 
  • #3
Hi, thanks for the help.. But one qn though. What will the value of [tex](\delta \theta) [/tex] be? Is it 5? But i though for this to apply, ur change has got to be small? i calculated the value of [tex](\delta \theta) ~sin(\theta)[/tex] and it is very big? Even bigger than the real value?
 
Last edited:
  • #4
gunblaze said:
Hi, thanks for the help.. But one qn though. What will the value of [tex](\delta \theta) [/tex] be? Is it 5? But i though for this to apply, ur change has got to be small? i calculated the value of [tex](\delta \theta) ~sin(\theta)[/tex] and it is very big? Even bigger than the real value?
[tex](\delta \theta) [/tex] has to be in radians. It would not be 5. Even so, it is possible for the uncertainty to be bigger than the value. For θ very near 90°, cos(θ) is near zero and sin(θ) is nearly 1, so the error would be about [tex](\delta \theta) [/tex], which could easily be bigger than cos(θ) even when expressed properly in radians.
 

1. How do I find the value of cos(theta) if I know the value of theta?

To find the value of cos(theta), you can use a scientific calculator or refer to a trigonometric table. Simply enter the value of theta and press the "cos" button on the calculator to get the corresponding value of cos(theta). If using a table, locate the row with the value of theta and then find the corresponding value of cos(theta) in the adjacent column.

2. Can I find the value of cos(theta) without using a calculator or table?

Yes, you can use the unit circle to find the value of cos(theta). The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. The x-coordinate of the point where the terminal side of an angle intersects the unit circle represents the value of cos(theta).

3. What is the range of values for cos(theta)?

The range of values for cos(theta) is between -1 and 1. This means that cos(theta) can take on any value between -1 and 1, including decimal numbers and fractions.

4. How does the value of theta affect the value of cos(theta)?

The value of theta affects the value of cos(theta) because it determines the position of the terminal side of the angle on the unit circle. As the value of theta increases, the terminal side moves around the unit circle and the value of cos(theta) changes accordingly.

5. Can I find the value of cos(theta) for any angle?

Yes, you can find the value of cos(theta) for any angle, whether it is acute, right, or obtuse. However, if the angle is greater than 360 degrees, you may need to use the concept of periodicity to determine the value of cos(theta).

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