I realize this is late, but if your up studying or check the blog early; this is very helpful. Look at this table. In section 1.4 the majority of degrees someone will get if they used the reference angle to find the exact value of a degree or radian will be either: 30, 45, or 60. Try it out in any of the problems we were assigned on that section and you will see. Now, most of the time we are told to set up a standard 45-45-90 triangle or 30-60-90 triangle; you can avoid ALL OF THAT if you memorize the Unit Circle Values for Sin, Cos, and Tan; since you can get their reciprocals: Cosecant, Secant, and Coterminal by for e.g. Cosecent = 1/Sin(x), or Secant = 1/ Cos(x), etc.
I hope this helps.
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