Now we are ready to learn the special case of the Sum and Difference Formulas: the Half-Angle Identities!
Remember when we discussed how 15 degrees can be expressed as 60 degrees minus 45 degrees, and then use a Sum and Difference Identity to calculate further?
Well, with Half-Angle identities we have yet another option!
Instead of using a sum or difference formula, we can now say that 15 degrees is half of 30 degrees, which is an angle on the Unit Circle!
Cool!
Yet another tool in your tool-belt!
So with the power of the Half Angle Formulas, we will once again learn how to evaluate trig functions of an angle that is not on the Unit Circle by finding one that is.
But wait a minute! So, with all of these identities (i.e., “tools”), how do I know which one to use?
Great question! Well, trick is knowing which type of identity is best to use, as Precalculus for Dummies accurately points out.
Sometimes it comes down to personal preference …. which one do you like best? or which one do you remember?
Half-Angle Identity Formulas
Other times, you will have to decipher the entire problem and see which one “fits” best. Don’t worry, it will be obvious and we’ll walk through all of this together!
In fact, not only will this lesson show you how to evaluate trig functions with the use of Half-Angle Identities, but we will also see how to prove some rather tricky identities as well. All in all, you will become a wiz at knowing which identity to use and when!
What is also important to note is that all of these identities that we are learning about, as fun and exciting as they are to use and prove, all play a pivotal role in many science and engineering applications, as accurately stated by Windstream, and are essential to success in Calculus.
Together we are going to fortify your knowledge and understanding of not only trigonometry so that you will be ready for all your future math courses.
Solving Half Angle Identities – Video
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