Essential Questions: What is a function? How is the sine definition different from the sine function? Cosine? Tangent? From the graph of these functions, list some properties that describe them? Rebecca Adcock, a former student of EMAT 6690 at The University of Georgia, and I agree that the concept of the Sine, Cosine Functions will occur at lesson 6 of a beginning trigonometry unit. I praise her and her work because I want to use her thoughts on this particular lesson and build upon it with the tangent function.
Please notice what we mean by a function and connecting this with the values along the unit circle.
After Rebecca’s lesson, you should know exactly what the sine and cosine functions look like. Below is a summary of this information.
Notice that the sine goes through the origin and travels to a maximum at (π/2, 1). Then, it travels down through (π, 0) to a minimum at (3π/2, -1). Finally the sine travels back up to (2π, 0). Then the sine wave will continue this same process again. Thus, the period of the sine function is 2π. Its amplitude is 1. Recall that sin (-x) = -sin x. This means that the sine function is odd, or it is symmetric to the origin.
Notice that the cosine goes through (0, 1), its maximum, to (π/2, 0) and down to (π, -1), its minimum. The cosine then travels back up through (3π/2, 0) and to (2π, 1). Then the cosine wave will continue this same process again. Thus, the period of the cosine function is also 2π. Its amplitude is 1. Recall that cos (-x) = cos x. This means that the cosine function is even, or it is symmetric to the y-axis.
1. Give the domain and range of the sine and cosine functions. 2. What are the maximum and minimum values of these functions? 3. Identify the y-intercept and zeros of each function.
4. Identify which function is odd and which one is even....