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
$$cos (\theta \pm \delta \theta) \approx cos(\theta) \pm (\delta \theta) ~sin(\theta)$$
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.