Test: Unit 6 (Graphs of Trig Functions)

(a)What is the amplitude?

(b) What is the period?

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Tags

CCSS.HSF-IF.C.7E

What is the period of  $y=9\cos\left(5\pi x\ +\ \frac{3\pi}{2}\right)-9$  ? Give an exact value. 

• π/3 or 60 degrees

• 6π or 1080 degrees

• 2π/3 or 120 degrees

• 3π or 540 degrees

Tags

CCSS.HSF-IF.C.7E

The ______________ measures the distance from the midline to the max or min of the function.

The _______________ is inversely proportional to the period of a sinusoidal function.

The _________________ represents the same value as the vertical translation.

A negative value of ______________ causes a _______________ in the graph of the function.

The amount of time for a function to complete its cycle is known as its _______________.

The horizontal translation is also known as a ________________.

• Amplitude

• Phase Shift

• Vertical Translation

• Horizantal Translation

Tags

CCSS.HSF-IF.C.7E

What is the equation of the graph?

•  y = 2 cos x
• y = sin x
• y = 2 sin x
• y = sin 2x 

Tags

CCSS.HSF-IF.C.7E

Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

• y = 5cos(x - pi) + 3
• y = 3cos(x - pi) + 5
• y = 3cos(2x - pi) + 5
• y = 5cos(2x - pi) + 3

Tags

CCSS.HSF-IF.C.7E

Below is the graph of a trigonometric function. It intersects its midline at (-1.7,-10) and again at (5.1,-10). What is the period of the function? Give an exact value.

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Tags

CCSS.HSF-IF.C.7E

Valeria is playing with her accordion.

The length of the accordion A(t) after she starts playing as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a⋅cos(b⋅t)+d

At t= 0, when she starts playing, the accordion is 20 cm long, which is the shortest it gets. 1.8 seconds later the accordion is at its average length of 42 cm.

Find A(t). Also draw the graph of the function, clearly showing 5 critical points.

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The graph below shows the parent function for cosine.
Sketch the graph of the transformed function given by
 $-0.5\cos\left(\frac{1}{3}x+\frac{\pi}{3}\right)-2$  

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Tags

CCSS.HSF-IF.C.7E

Below is the graph of a sinusoidal function. The maximum point is shown, and it has an amplitude of 4.6. What is the equation of the midline?

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Tags

CCSS.HSF-IF.C.7E

What is the equation of graph? 

• y = sin 5x
• y =  cos 5x
• y = 5 sin x
• y = 5 cos x 

Tags

CCSS.HSF-IF.C.7E