"In order to simplify problems in physics, we often use various approximations. For example, when we investigate diffraction and interference patterns at small angles θ, we frequently approximate sinθ and tanθ by θ (in radians). Here you will calculate over what range these are reasonable approximations.
For θ= 43° this approximation has an error of almost exactly 10%:
θ = 43.0° = 0.75 radians
|sinθ-θ| / |sinθ| ≈ 10%"
1) For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 5%?
2) For what value of θ (to the nearest degree) is the error in tanθ ≈ θ approximately 5%?
I was recently given this question and very little explanation of the concept. I've struggled with this for a week and read absolutely everything I can find and I'm still not any closer to understanding it. Can anyone please point me in the right direction or explain how to do question 1) and 2)? There are many more questions, but if I can get 1) and 2) down then I should be able to answer the rest by myself. I appreciate any help.
The Attempt at a Solution