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Trigonometry, SPEC2 2021 VCAA 3 MC

The coordinates of the local maxima of the graph of  `y = 1/((cos(ax) + 1)^2 + 3)`, where  `a ∈ Rtext(\){0}`, are

  1. `((2pik)/a , 1/7), k ∈ Z`
  2. `((2pik)/a , 1/3), k ∈ Z`
  3. `(((1 + 2k)pi)/(2a) , 1/4), k ∈ Z`
  4. `((pi(1 + 2k))/a , 1/4), k ∈ Z`
  5. `((pi(1 + 2k))/a , 1/3), k ∈ Z`
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`E`

Show Worked Solution

`y_text(max)\ \ text(occurs when)`

Mean mark 51%.

`(cos(ax))^2 + 3\ \ text(is a minimum)`
 

`text(Find)\ x\ text(such that:)`

`cos(ax)` `= -1`
`ax` `= pi + 2kpi, k ∈ Z`
`x` `= (pi(1 + 2k))/a`

 
`:.\ text(Local maxima at)\ ((pi(1 + 2k))/a, 1/3)`

`=>\ E`