First off, this post is actually by AmyR, I just lost my password.
Need a nifty radian circle to compare degrees to radians to trig ratios? Of course!
This shows the complete relationship between the three values in a neat visual way. For anyone who has struggled with this topic, I highly suggest you print yourself off a copy of this circle and study them! There is really only three values that you have to memorize, so once you understand the pattern the sinusoid has, the three values are easy.
Ratios tend to be the must challenging to memorize, but they should be memorized. There are only three values, and knowing them is more helpful than having to solve for them every time. The values are 1/2, ?2/2, and ?3/2. The values are in increasing value. If you familiarize yourself with this order, the ratios become easy. If sine starts at 0 and has to increase, the next value will be the closest to 0. Which one is that? 1/2 of course! Then comes the next smallest, since it goes even higher, which would be ?2/2.
What about cosine at 210 degrees? Well, if cosine is 1 at 0 degrees, and is -1 at 180 degrees, at 210 degrees it is probably making its climb back up to the x axis. So what value is slightly greater than -1? -?3/2! Once you understand the patterns and qualities of sinusoidal graphs, finding the ratio value isn’t that difficult. There are five options you have, two of them (0 and 1) should already be obvious. 0, 1/2, ?2/2, ?3/2, and 1 are you ratio values.
I hope this was beneficial to some of you, the people that I have helped who have had trouble with this tend to find this method easy and convenient.
Enjoy the new semester you guys!