Question

2.) Which of the following functions have graphs that oscillate? Select all that apple (2 points)

A.) y = sin θ
B.) y = cos θ
C.) y = tan θ
D.) y = sec θ
E.) y = csc θ
F.) y = cot θ

4.) Which of the following have a vertical asymptote for values of θ such that cos θ = 1? Select all that apply. (2 points)

A.) y = sin θ
B.) y = cos θ
C.) y = tan θ
D.) y = sec θ
E.) y = csc θ
F.) y = cot θ

Update! I finally figured it out; Here are the answers to it all.

1.) C
2.) A and B
3.) C
4.) C and D

Answer 1

For the last one, It's actually E and F. 

Answer 2

2) Option A and B

4) Option E and F

Explanation:

2) Which of the following functions have graphs that oscillate?

A.) y = sin θ

B.) y = cos θ

C.) y = tan θ

D.) y = sec θ

E.) y = csc θ

F.) y = cot θ

Oscillation is a periodic movement between two points.

From the above options only sin θ and cos θ oscillates between two points.

Refer the attached graph below.

Therefore option A and B are correct.

4) Which of the following have a vertical asymptote for values of θ such that cos θ = 1?

The vertical asymptote is a vertical line that the graph of a function approaches but never touches or not defined.

Since, cos θ = 1

θ = 0 as cos θ = cos 0

Now, we put the value and determine the behavior.

A.) y = sin θ = sin 0 = 0

B.) y = cos θ = cos 0 =1

C.) y = tan θ = tan 0 = 0

D.) y = sec θ = sec 0 = 0

E.) y = csc θ = csc 0 = not defined

F.) y = cot θ = cot 0 = not defined

Therefore, Option E and F are correct.