How do i find the value of cos(theta)

[gunblaze]

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.

 

[nrqed]

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
<br /> cos (\theta \pm \delta \theta) \approx cos(\theta) \pm (\delta \theta) ~sin(\theta)
where you must use \delta \theta in radians .

Hope this helps.

Patrick

 

[gunblaze]

Hi, thanks for the help.. But one qn though. What will the value of (\delta \theta) be? Is it 5? But i though for this to apply, ur change has got to be small? i calculated the value of (\delta \theta) ~sin(\theta) and it is very big? Even bigger than the real value?

 

[OlderDan]

Hi, thanks for the help.. But one qn though. What will the value of (\delta \theta) be? Is it 5? But i though for this to apply, ur change has got to be small? i calculated the value of (\delta \theta) ~sin(\theta) and it is very big? Even bigger than the real value?

(\delta \theta) 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 (\delta \theta), which could easily be bigger than cos(θ) even when expressed properly in radians.