Question

Please do not skip steps, and include show your work for both problems.

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° = 0.75 radians

sinθ=0.682

|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 sinθ ≈ θ approximately 1%?

Answer 1