Question

My question is a two-parter. The first deals with the geometric proof of the derivative of sin(x) from Session 8, and the second deals with the nature of this site (first question!).

Both the video lecture and the notes are a little vague about proving that the angle QPR = theta. The professor talks about rotating the horizontal line by 90 degrees, but after that the language gets so vague that I failed to follow the "proof" that the angles are the same. Can anyone clarify?

Question 2: Is there any decent way to search for questions that were previously asked? Seems silly to ask twice :)

Answer 1

Hey Duckbill, welcome!

First of all, there is no built in method for searching for answers on OpenStudy (yet). However, if you go to google, and type the following "site:openstudy.com" after your keyword search, you will accomplish a site search which is very helpful sometimes!

As for the geometric question: I've simplified the picture from the lecture by removing the points of interest and exending the vertical line PR

Answer 2

Your question involves demonstrating that: \[x= \theta\] in the picture above. Notice that a line is pi radians, as is a triangle. Also, a right angle has pi/2 radians. From there:
\[\beta = \frac{pi}{2} - \theta\\ \theta = \frac{\pi}{2} - \beta\\ x = \pi - \frac{\pi}{2} - \beta\\ x = \frac{\pi}{2} - \beta = \theta\]