In response to your question: I am an ACE certified personal trainer and former powerlifter with a best squat (to a depth that is deeper than 90 degrees) of 585lbs. I squated between 1 and 2 times per week with a weekly squat volume of between 5,000 and 8,000 lbs. total. I actually had less knee pain as i got stronger! I could never have done this if i had not discovered the box squat and the technique that accompanies it. Follow the link that was listed above or go to Elitefts.com and search for it. The box squat is not the end all in the world of squatting, but it is a great teaching tool. In my experience, most people squat with terrible form, because they have never been taught to squat properly...unless your high school gym class had powerlifting as an elective.
Until i learned good form i could never squat more than 300lbs and that was accompanied by massive knee sorness. Find someone who knows their stuff and get some help. once you learn to squat properly, you will reap the rewards of possibly the best weight room exercise. By the way, 90 degrees should be fine for most healthy adults with propper form. for most people this means a box hight of around 14-16 inches (but only after you get comfortable with the box squat technique). You will know if you are squatting propperly when your hamstrings lower back (spinal erectors) and glutes feel sore and tired as squatting propperly will activate these muscles majorly (and the quads will feel less lactic acid soreness).
Not like us cyclists need more muscle imballances. so training the hammies and glutes is quite valuable. good luck, take it slow.