Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences? Be sure and include the phase shift that would make the graphs congruent to each other.
Part 2: Describe the function, f(x) = 5 sin(2x - π) + 3, using the vocabulary of this chapter. For full credit be sure to include some description of the key words. That is saying the Amplitude is 5, is only C work.

Question

Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences?  Be sure and include the phase shift that would make the graphs congruent to each other.
Part 2: Describe the function, f(x) = 5 sin(2x - π) + 3, using the vocabulary of this chapter.  For full credit be sure to include some description of the key words.  That is saying the Amplitude is 5, is only C work.

anonymous · Answer

Part 1:
1. The sine graph passes through the origin while the cosine graph intercepts the y-axis at (1, 0).
2. Both the sine and cosine graphs have a period of 2pi and an amplitude of 1
3. Both the graphs are continuous curves that have a domain of (-infinity, infinity) and a range of [-1, 1]
4. There is a phase difference of pi, that is 90 degrees between the graphs. This means that if the graph of sine or cosine is shifted right or left by pi units on the x-axis, both the graphs become congruent.

Does that help?