1. The problem statement, all variables and given/known data 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% For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 5%? 2. Relevant equations |sinθ-θ| / |sinθ| ≈ 10% 3. The attempt at a solution So I was not having much luck finding the approximate for 5% so i tried to work backwards with the .75 radians and 10%. I set it up like |sin.75-.75| / |sin.75| ≈ 10% which works...so i tried to use the CAS calculator to quick solve the other question and I had no such luck. I attempted to have it solve |sinx-x| / |sinx| = .1...and it gave me an answer of false. I did get the right answer...but I literally just plugged in numbers until it worked out. I was wondering first if there is a better way to solve this not using CAS and second why didn't the CAS system work?