Symbolab Summer Collection or how to symbolab trigonometric equations

When solving trigonometric equations you should be familiar with algebraic manipulations, basic geometry, triangles and more triangles, the six trigonometric ratios, trigonometric identities, trigonometric manipulations, radians, degrees and the unit circle. That’s quite a lot to remember.

To complicate things if there is one solution then there are an infinite number of solutions; trigonometric functions are periodic.

Trying to simplify things, the goal is to isolate the trigonometric function (using the scary list from above).  To simplify even more, we are now solving trigonometric equations step by step.   Let’s take a look at a few examples:

Example using trigonometric identities (click here):

Example using basic Algebraic manipulations (click here):

Stay tuned, we have more trig coming your way

Cheers,
Michal

I know what you did last summer…Trigonometric Proofs

To prove a trigonometric identity you have to show that one side of the equation can be transformed into the other side of the equation.  This usually requires turning everything into sines and cosines, some algebraic manipulations (join fractions, expand, factor, etc.) and use of fundamental trigonometric identities.  Sounds familiar? Not really, it is very different than solving equations.   You have to work on one side at a time, so algebraic properties that work on both sides of the equation can’t be used.   Complicated? Yes… but the good news about proofs is that you always know where you are going…

…and the real good news is that we are now doing it for you!  Just say the magic word (Prove, not please), type in the trig identity, press Go, and wow, a step by step poof coming your way.

Let’s start with a few examples.  With time (and practice) you’ll learn the best tricks to use and the identities that are most helpful (the Pythagorean identity is a favorite)

Example expressing with sine and cosine, Join, Factor and Pythagorean identity (click here)

Example using fraction multiplication trick (click here)

Enjoy the rest of the summer!
Michal