SP #7: Unit Q Concept 2 - Finding All Trigonometric Functions Using Identities

This SP #7 was made in collaboration with Sergio Sanchez. Please visit the other awesome posts on their blog by going here.

Our given is:

One of the first and foremost steps that must be undertaken, is identifying which quadrant we are working with. Although, using the values of the trig functions and their accompanied signs would do just as well.

Next, we'd just go right into solving this with trigonometric identities. It's pretty self-explanatory had one taken this course. But, for the sake of something: first, I list out the identity, and then, substitute in the value(s) that I already have. I then solve it until there is one unknown trigonometric function is on one side, and a value is on the other.

As for Sergio's work, I suppose that I shall put forth some sort of explanation, in lieu of the original creator, who just gave me this picture. Basically, he plugged in values that were given (from the tangent trigonometric function), into the Pythagorean Theorem, in order to get the excluded side's value. Having gotten all of the sides, he just plugged them into the rest of the unknown trigonometric functions.

It is important that one remembers what all of the trigonometric functions mean - what sides they represent, and how they represent each other. As in, you have to remember that sine is opposite / hypotenuse, and also, 1 / secant. This is important because if you could fail pretty easily if you use the wrong functions/identities. It's also very important for one to remember to rationalize (which I did), and reduce (which I didn't do). Apparently, it's the most important thing you could do for yourself, for forgetting to do so, would result in loss of points on your tests or whatever.