5-6 Double and Half Argument Properties

Hooray! I'm so excited that it's my turn to blog once again!

Now that we have learned all about all the other properties in the chapter, it is time to learn some more. This section focuses on the double and half argument properties.

You use the double argument properties when you are writing cos2x or cos(x+x), and the other trigonometric functions. Similarly, from these double argument properties, you can derive the half argument properties.

We use these properties for many different purposes, including finding the exact values without the use of our calculators....

Here are the properties in this section:

The Products and Squares of Cosine and Sine


We use thes when you have a sine and a cosine, or two cosines and two sines.










Example of when you use the products and squares of cosine and sine:










The Double Argument Properties (the important part)
note: we have to memorize the sine and cosine equations

Double Argument Property for Sine
sin 2A = 2sinAcosA

Double Argument Properties for Cosine
(yes, there are multiple equations for cosine)








Double Argument Properties for Tangent
(although we don't have to know it)






Example of when you use the double argument properties:






The Half Argument Properties for Sine, Cosine, and Tangent

Example of how to use the half argument property:

Find the exact value of sin 15° → think of it as half of 30

choose the positive because the angle is in the first quadrant, where sin is positive

So...basically, that's the lesson!

Here is a link just incase you want some extra help.... http://www.math.ucdavis.edu/~marx/doubang2Pr/doubang2Pr.html

My Favorite Part...the personalization!

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and also....

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a picture to show you the goodness...

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Paul...you are next!!!