Question

1 matching 1 point
match each given definition with the correct word it defines.
the height of the graph from the midline
the length of a cycle
2 multiple choice 1 point
on the function $y = a\sin(b\theta)$, what is the following called: $|a|$?
frequency
amplitude
midline
amplitude
period
horizontal phase shift

Explanation:

Question 1 (Matching)

For the definition "The length of a cycle", in the context of periodic functions (like sine or cosine graphs), the term that represents the length of one complete cycle is "Period".

In the function \( y = a\sin(b\theta) \), the amplitude of a sine function is defined as the absolute value of the coefficient \( a \), i.e., \( |a| \). Frequency is related to \( b \) (frequency \(=\frac{b}{2\pi}\) for \( y = a\sin(b\theta) \)), so \( |a| \) is the amplitude.

Answer:

The length of a cycle - Period

Question 2 (Multiple Choice)