I'm self-studying pre-calculus right now and have run up on a huge bump in the hill. I'm really slow at recalling the values of trig functions on the unit circle given an angle. For instance csc(π/3) may take me upwards of 20-30 seconds because I'm so slow at recalling it. I'm usually very quick when it comes to math, but for the past two days I've tried improving my speed and have only made slight increases in speed.
My current algorithm goes like this :
1.) Recall the non-reciprocal function's ratio
2.) Flip this
3.) Rationalize the ratio if needed
My problem is for some reason panicking and suddenly taking 5 seconds to figure out if csc is the reciprocal of sin or cos, even though I have practiced forever that it is sin's. Then sometimes, despite me knowing the sin and cos ratios very well, struggle with getting my brain to remember where I'm searching (like what angle I'm looking for). Finally, I sometimes freeze up and can't do the simple rationalization once I flip it.
I made flash cards but they don't seem to help me so much. I'm really frustrated and stuck and seem to have some mental problem happening. Usually this stuff is really easy for me to get good at, but I'm having an incredibly difficult time getting good at it. Do you have any advice? Thanks