Transformations of Trigonometric Functions

Assuming no transformation what is this function?

• y=sin(x)

• y=cos(x)

• y=tan(x)

• Neither

The _________ measures the distance from the midline to the maximum or minimum of the function.

• Horizontal shift

• Vertical shift

• Period

• Amplitude

The period of  $y=a\sin\left(bx\right)+d$  is...

• a

• b

• d

• None of the above

The horizontal length required to complete one cycle is called...

• Amplitude

• Cycle

• Horizontal shift

• Period

Which of the parameters represents the horizontal translation of $y=a\cos\left(bx-c\right)+d$  ?

• a

• b

• d

• d

• None of the above

What is the amplitude of  $y=-3\sin\left(2x\right)-4$  ?

• –3

• 3

• 2

• –4

• 4

What is the period of  $y=4\cos\left(2x\right)+1$ ?

• 4

• 2

•  $\pi$  

•  $2\pi$  

• 1

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.4

Write a cosine function for the graph shown here.

Write a sine function for the graph shown here.

A transformed sine function has amplitude of 4, and takes 5 units to complete a cycle. It also has a vertical translation of 2 units to the right, a horizontal translation of 3 units down. Write the equation of this sine function.