That is because theta is approximately equal to sine theta (when you calculate in radians). I dunno if you heard about the the standard limit((sinx)/x) when x->0 the limit approaches 1. So that’s why, also the difference usually becomes significant when the angles exceeds more than 5-10 degrees.
![Single Slit Diffraction [AHL] - IB Physics](http://i.ytimg.com/vi/JqSm-gI6opo/mqdefault.jpg)
![Single Slit Diffraction [AHL] - IB Physics](/img/tr.png)
Why did you consider only theta in the first question and in the second question you took sin(theta)? Please tell the difference.
At small angles both are same. Sometime we take theta sometimes sin theta depending on which one simplifies the question
That is because theta is approximately equal to sine theta (when you calculate in radians). I dunno if you heard about the the standard limit((sinx)/x) when x->0 the limit approaches 1. So that’s why, also the difference usually becomes significant when the angles exceeds more than 5-10 degrees.