Graphs of Sine and Cosine

Graphs of Sine and Cosine

Make an xy-table

​

How the graph is constructed

• x-intercepts at x=0,

  x=π, x​=2π

• Maximum at x=π/2

• Minimum at x= 3π/2

Key elements

• It has a period of 2π

• It has an amplitude of 1

• A cycle starts at y=0 and ends at y=0

• Ends at x​=2π

• Domain is all the reals

• Range is [-1, 1]

Periodic Function

• x-intercepts at x=π/2 and x​=3π/2

• Maximum at x=0

• Minimum at x= π

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​Cosine Function

• It has a period of 2π

• It has an amplitude of 1

• A cycle starts at y=1 and ends at y=1

• Domain is all the reals

• Range is [-1, 1]

Periodic Function

Multiple Choice

Sine or Cosine?

• y=sinx
• y=cosx

Drag and Drop

The __________ represents half the distance between the max and min of a sine or cosine graph. 

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Period

Frequency

Extreme Values

Amplitude

Multiple Choice

What is the domain and range of $$y=\sin x$$ ?

• D: (-∞, ∞)
  R: [-1, 1]
  
• D: (-∞, ∞)
  R: [-π, π]
• D: (∞, -∞)
  R: [-1, 1]
  
• D: (-∞, ∞)
  R: [-∞, ∞]
  

Multiple Choice

What is the domain and range of $$y=\cos x$$ ?

• D: (-∞, ∞)
  R: [-1, 1]
  
• D: (-∞, ∞)
  R: [-π, π]
• D: (∞, -∞)
  R: [-1, 1]
  
• D: (-∞, ∞)
  R: [-∞, ∞]
  

Drag and Drop

What is the equation of the graph?

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y = sin x

y = - sin x

y = cos x

y = - cos x

Multiple Choice

Sine or Cosine?

• $$y=\sin x$$

• $$y=\cos x$$

Drag and Drop

The __________ represents the x-distance between the start to the end of a cycle of a sine or cosine graph. 

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Period

Frequency

Extreme Values

Amplitude

Drag and Drop

The __________ represents the number of cycles a sine or cosine graph has in a 2π range

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Period

Frequency

Extreme Values

Amplitude

Multiple Choice

Calculate the amplitude of the curve

• $$2\pi$$

• 2

• 1

• 0

Multiple Choice

Calculate the period of the curve

• $$4\pi$$  

• $$2\pi$$

• 2

• 0

Drag and Drop

Calculate the period of the curve

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Drag and Drop

What is the amplitude of the graph? 

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1

3

6

9

Drag and Drop

Which trig function does this graph represent?

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csc

sec

cos

sin

Drag and Drop

Which trig function does this graph represent?

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csc

sec

cos

sin

Drag and Drop

Which trig function does this graph represent?

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csc

sec

cos

sin

Drag and Drop

Which trig function does this graph represent?

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csc

sec

cos

sin

Drag and Drop

What is the period?

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4π

2π

π

8π

Drag and Drop

What is the period? ​

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2π

4π

8π

Drag and Drop

Which graph is it?​ ​

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positive cosine

positive sine

negative cosine

negative sine

Drag and Drop

Which graph is it?​

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negative cosine

positive cosine

negative sine

positive sine