**This is a post summarizing the basic properties of the cosine and sine functions.**

**Here is the cosine function and its properties:**

**In this example:**

**h is 0;**

**k and L are 3;**

**b and P are 2π and**

**a is 2.**

**And here is the sine function and its properties:**

**In this example:**

**h is -π/2;**

**k and L are 3;**

**b and P are π and**

**a is 2.**

**The parameter h is rather simple, as its affect doesn't change throughout the various functions we've learned this year. The a, b and k parameters and the new**

*parts*like the period and the line of oscillation (the*middle*or*mid-point*of the function) are different. They can be determined by the naked eye or with these formulas:

**The "M" and "m" in this case are the "maximum" and "minimum" of the function in question. Notice that L and k have the same formula, so it isn't necessary to find both as finding one will automatically find the other.**

**Don't let yourself get fooled by the period and frequency in this example for they are**

__not the same__. Frequency is how*long*a function is (from the beginning of the tulip/snake to the end of it) and the period is the amount of*2π-*

*segments*within the whole frequency. It just so happens that this example has a frequency of 1, which is why we do not see a b in the functions stated in the example images.

**Here are two additional formulas you may find useful:**

**Thank-you and please share your thoughts in the comments section! :)**

Wow. This is a great summary! Loving all the colors and your background! You really broke down all of the key elements and formulas of these functions! Will definitely use this for memory aids and notes if you don't mind (:(: Thanks!

ReplyDeleteOh well I don't mind at all actually! I'm glad you like it! :D

DeleteThis is an awesome review! you explain cos and sin properties very well and make it really easy to understand and remember! thanks! Kaitlyn's right, this will come in handy for my memory aid :D

ReplyDeleteWell Laura, I'm happy it helped you. I'm also happy you liked this post! :)

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