Sine, Cosine, and Tangent Functions

Essential Questions: В Just what function? В How may be the sine definition different from the sine function? Cosine? Tangent? В In the graph of those functions, list some homes that describe them? В Rebecca Adcock, a former student of EMAT 6690 at The University or college of Atlanta, and I consent that the idea of the Sine, Cosine Capabilities will happen at lesson 6 of your beginning trigonometry unit. В I reward her and her operate because I wish to use her thoughts on this kind of lesson and create upon it with the tangent function. В В

You should notice that which we mean by a function and connecting this kind of with the values along the unit circle. В

After Rebecca's lesson, you have to know exactly what the sine and cosine functions look like. В Below is a summary of this information. В

Sine Function


Observe that the sine goes through the origin and travels to a optimum at (ПЂ/2, 1). В Then, that travels down through (ПЂ, 0) to a minimum at (3ПЂ/2, -1). В В Finally the sine trips back up to (2ПЂ, 0). В Then the sine wave is going to continue a similar process once again. В As a result, the period of the sine function is 2ПЂ. В Their amplitude is 1 . В Recall that sin (-x) = -sin x. В This means that the sine function is unusual, or it is symmetric to the source. В В

Cosine Function


Realize that the cosine goes through (0, 1), it is maximum, to (ПЂ/2, 0) and down to (ПЂ, -1), its lowest. В The cosine in that case travels back up through (3ПЂ/2, 0) also to (2ПЂ, 1). В Then a cosine wave will continue this same procedure again. В Thus, the time of the cosine function is additionally 2ПЂ. В Its exuberance is 1 . В Recollect that cos (-x) sama dengan cos x. В Which means that the cosine function is usually even, or it is symmetric towards the y-axis. В

Student Activity:

1 . Provide the domain and range of the sine and cosine features. 2 . Precisely what are the maximum and minimum beliefs of these features? 3. Identify the y-intercept and zeros of each function.

4. Discover which function is unusual and which is actually....