Which of the following functions have graphs that oscillate? Select all that apply.

Question

(1 point)
Responses

y = sin θ
y = sin θ

y = cos θ
y = cos θ

y = tan θ
y = tan θ

y = sec θ
y = sec θ

y = csc θ
y = csc θ

y = cot θ

Answer 1

The functions that have graphs that oscillate (i.e., graphs that repeat their values in a periodic manner) are:

• \( y = \sin \theta \)
• \( y = \cos \theta \)

The other functions, \( y = \tan \theta \), \( y = \sec \theta \), \( y = \csc \theta \), and \( y = \cot \theta \), do not oscillate in the same way as sine and cosine; instead, they have asymptotic behavior (approaching infinity) at certain points.

So the correct responses are:

• \( y = \sin \theta \)
• \( y = \cos \theta \)