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Trigonometry, 2ADV T3 SM-Bank 8 MC

The diagram below shows one cycle of a circular function.
 

The amplitude and period of this function are respectively

  1. `3\ \ text(and)\ \ 2 `
  2. `3\ \ text(and)\ \ (pi)/(2)`
  3. `4\ \ text(and)\ \ (pi)/(4)`
  4. `3\ \ text(and)\ \ 4`
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`D`

Show Worked Solution

`text(Graph centres around)\ \ y = 1`

`text(Amplitude) \ = 3`

`text(Period:) = 4`

`=> D`

Filed Under: Trig Graphs (Y12) Tagged With: Band 3, smc-977-40-Unknown Trig Ratio

Trigonometry, 2ADV T3 SM-Bank 7 MC

met2-2011-vcaa-15-mc 
 

The graph shown could have equation

  1. `y = 2cos(x + pi/6) + 1`
  2. `y = 2cos4(x - pi/6) + 1`
  3. `y = 4sin2(x - pi/12) - 1`
  4. `y = 3cos(2x + pi/6) - 1`
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`=> B`

Show Worked Solution

`text{Amplitude = 2   (range from – 1 to 3)}`

`text{Graph centre line (median):}\ \ y= 1`

`:.\ text(Eliminate)\ \ C\ \ text(and)\ \ D.`
 

`text(Period) = (2pi)/3 – pi/6 = pi/2\ \ text{(from graph)}`

`text(Consider option)\ B,`

`text(Period)= (2pi)/n= (2pi)/4 = pi/2`

`=> B`

Filed Under: Trig Graphs (Y12) Tagged With: Band 4, smc-977-40-Unknown Trig Ratio

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