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In this lesson, we will learn how to derive the amplitude, period, midline, and horizontal and vertical shifts of a trigonometric function from its equation.

Q1:

Which function is represented on the graph?

Q2:

What is the maximum value of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 ( 𝑥 − ℎ ) ) + 𝑘 s i n ?

Q3:

What is the amplitude of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 ( 𝑥 − ℎ ) ) + 𝑘 s i n ?

Q4:

Simplify c o s ( 1 8 0 − 𝜃 ) ∘ .

Q5:

What is the midline of 𝑦 = 𝑥 s i n ?

Q6:

The figure shows the graph of 𝑦 = 𝑥 s i n .

Which of the following is a graph of 𝑦 = 2 𝑥 s i n ?

Q7:

Which of the following is a graph of 𝑦 = ( 𝑥 ) + 2 s i n ?

Q8:

Which of the plots shown in the graph represents the tangent function?

Q9:

What is the amplitude of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 𝑥 − 𝑐 ) + 𝑘 c o s ?

Q10:

Let 𝑓 ( 𝑥 ) = 2 𝑥 s i n . What is the smallest positive value of 𝑃 for which 𝑓 ( 𝑥 + 𝑃 ) = 𝑓 ( 𝑥 ) holds?

Q11:

Simplify s i n ( 1 8 0 − 𝜃 ) ∘ .

Q12:

Simplify s i n ( 3 6 0 − 𝜃 ) ∘ .

Q13:

The figure shows the graph of a periodic function.

The height of the function’s midline was doubled. Which of the following is the graph of the resulting function?

Q14: