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Trigonometry, 2ADV T3 2010 MET1 3

Shown below is part of the graph of a period of the function of the form  `y = tan(ax + b)`.
 


 

Find the value of `a` and the value of `b`, where  `a > 0`  and  `0 < b < 1`.  (3 marks)

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`a = (7pi)/24, b = pi/24`

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`y = tan(ax + b)`

`text(Substitute)\ \ (1, sqrt3), (−1, −1)\ \ text(into equation:)`

`tan(a + b)` `= sqrt3`
`tan(b – a)` `= −1`
`a + b` `= pi/3 \ …\ (1)`
`b – a` `= −pi/4 \ …\ (2)`

 
`text{Add (1) + (2):}`

`2b` `= pi/3 – pi/4`
`b` `= pi/24`

 
`text{Substitute into (1):}`

`a + pi/24` `= pi/3`
`a` `= (7pi)/24`

Trigonometry, 2ADV T3 SM-Bank 4 MC

A section of the graph of  `f(x)`  is shown below.
 

VCAA 2012 6mc
 

The equation of  `f(x)`  could be

  1. `f (x) = tan (x)`
  2. `f (x) = tan (x - pi/4)`
  3. `f (x) = tan(2 (x - pi/4))`
  4. `f (x) = tan(2 (x - pi/2))`
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`C`

Show Worked Solution

`text(Period) = pi/2`

`=>\ text(must be)\ C\ text(or)\ D`

`text(Shift)\ \ y = tan(x)\ \ text(right)\ \ pi/4.`

`=>   C`