CPM Homework Help : PC Problem 4-38

ARE SINE AND COSINE PARENT GRAPHS?

Although sine and cosine have the shape and one can be transformed by a shift to create the other, we will consider them both parent graphs. We have determined the domain and range for both functions. Complete the investigation by answering the following questions:

What is the period for $y =\text{sin }x$ and $y =\text{cos }x$ ?
What is the amplitude for $y =\text{sin }x$ and $y =\text{cos }x$ ?
What are the intercepts for $y =\text{sin }x$ ?
What are the intercepts for $y =\text{cos }x$ ?

Hint:

Use the graphs below to find the answers for (a) - (d).
2 waves, blue labeled, y = sine of x, has 5 turning points, @ (negative 5 halves pi, comma negative 1), (negative 3 halves pi, comma 1), (negative 1 half pi, comma negative 1), (1 half pi, comma 1), & 3 halves pi, comma negative 1), orange labeled, y = cosine of x has 4 turning points, @ (negative 3 pi, comma negative 1), (negative 2 pi, comma 1), (negataive pi, coomma negative 1), (0, comma 1), (pi, comma negative 1), & (2 pi, comma 1).

Hint (a):

The $x$ distance for $1$ whole cycle.
Added to the 2 waves, horizontal blue arrow between (negative 2 pi, comma 0), & (negative pi, comma 0), & horizontal orange arrow between (negative pi, comma 0), & (pi, comma 0).

Hint (b)

Added to 2 waves, vertical arrow from (1 half pi, comma 0), to (1 half pi, comma 1).

Hint (c):

Write an expression for all intercepts.

Hint (d):

Write an expression for all intercepts.
Added to the 2 waves, orange points at the x intercepts of negative 5 halves pi, negative 3 halves pi, negative 1 half pi, 1 half pi, & 3 halves pi.