Do you like puzzles?
I love all types of puzzles: jigsaw puzzles, crossword puzzles, hidden pictures, you name it I find them fascinating.
Well, Proving Trigonometric Identities is a lot like solving a puzzle.
You are given the answer, just like you are given the picture of what your finished product should look like, and all you have to do is get there!
What if I don’t like puzzles? Is this going to be hard?
Proving, or verifying, trig identities can be tricky at times, but I assure you that with practice, perseverance, and some ingenuity, you’ll learn to love them.
Besides, I’m going to show you some awesome tricks and steps to help you become a trig identity ninja!
To prove a trigonometric identity, we must use clear, logical steps, as accurately stated by Purplemath. Remember, our main objective is to transform one side of an equation to look like the other side.
Simplifying Trig Identities Example
Wait a minute! This sounds a lot like those two-column proofs we did in Geometry, where we had to write down statements and reasons using theorem or postulate. Eek!
Take a sigh of relief, because Proving Trigonometric Identities isn’t anything like what you did in Geometry. You won’t need to write down statements or reasons because your work and logical steps stand in place of having to write theorems or reasons!
You can do a happy dance now!
Alright, so you should know that there are countless ways someone can manipulate and transform a trigonometric expressions, but this lesson, which is the first of two videos on proving/verifying trig identities, is designed to show you the tools that will enable you to arrive at your answer in the most efficient and easiest way possible.
Together we will become confident in the most important, and sometimes sneaky, manipulations and know when and how to use them.
We will practice how to factor all types of trigonometric expressions, review how to distribute, create common denominators for complicated fractions, and even use the conjugate in order to arrive at the answer we desire.
Understanding when and how to use these tricks is extremely important, for it is a big part of any trigonometry class, as Bright Hub Education points out, and will be used repeatedly in all future math classes – especially calculus!
Steps for Proving Trig Identities – Video
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