When working on determining exacts values of a trigonometric ratio, we are often face with most angles on the unit circle that are based on reference angle of either 30º- 60º- 90º The "special" nature of these triangles is their ability to yield exact answers instead of decimal approximations when dealing with trigonometric functions.
30º-60º-90º Triangle Pattern Formulas
Labeling:
H = hypotenuse
LL = long leg (across from 60º)
SL = short leg (across from 30º)
Find the exact value of
sin 45º + cot 45º
.
*An easy way of differentiating values for 30º-60º is in 30º adjacent is √3 and opposite is 1. While in 60º the values switches where adjacent if 1 and opposite is √3.*
For further help, if you already haven't done this, here is a small table of values of Trigonometric Functions in Isosceles Triangle, and Quadrantal Angles.
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Having done this brings you closer to finding the exact value where the next step is applying the appropriate Trigonometric Functions. With this info you should be able to figure out how to determine the exact coordinates for each P(θ) given.
Watching these videos really solidified my understanding of this unit because I get to hear how others explain it and I am able to piece together things much better having already learned the concept.
So that's pretty much it for what I have to say, I know its not much but these are things that made it easier for me to understand what is going on. I hope you guys can make something out of this and good luck in your studies!