Answer:
2) Option A and B
4) Option E and F
Step-by-step 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.
