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Trigonometry, EXT1 T1 EQ-Bank 5 MC

Which equation describes the graph shown?
 

  1. \(y=2 \cos ^{-1}(x+1)\)
  2. \(y= \sin ^{-1}(x-1)\)
  3. \(y=2 \cos ^{-1}(x-1)\)
  4. \(y=\dfrac{1}{2} \sin ^{-1}(x+1)\)
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\(C\)

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\(\text{Graph shape (general)}\ \ → \cos^{-1}(x) \)

\(\text{Graph translated 1 unit to the right}\ → \cos^{-1}(x-1) \)

\(\text{Range:}\ 0 \leq \cos^{-1}(x-1) \leq \pi\ \ →\ 0 \leq 2\cos^{-1}(x-1) \leq 2\pi \)

\(\Rightarrow C\)

Trigonometry, EXT1 T1 2013 HSC 9 MC

The diagram shows the graph of a function. 
 

2013 9 mc
 

 Which function does the graph represent? 

  1. `y = cos^(-1) x`
  2. `y = pi/2 + sin^(-1) x`
  3. `y = - cos^(-1) x`
  4. `y = - pi/2\ - sin^(-1) x`
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`B`

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`text(By elimination,)`

`text(The graph passes through)\ \ (1, pi)`

`text(The only equation to satisfy this point is)`

`y = pi/2 + sin^(-1) x`

`=>  B`

Trigonometry, EXT1 T1 2012 HSC 4 MC

Which function best describes the following graph? 

2012 4 mc

  1. `y = 3sin^(−1) 2x` 
  2. `y = 3/2 sin^(−1) 2x` 
  3. `y = 3sin^(−1)\ x/2` 
  4. `y = 3/2 sin^(−1)\ x/2` 
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`C`

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`text{Domain:}` `\ \ -2 <= x <= 2`
  `\ \ -1 <= x/2 <= 1`

 
`:.\ text(Graph is)\ \ y = a sin^(-1)\ x/2`
 

`text(When)\ \ x = 2,\ \ y = (3pi)/2:`

`(3pi)/2` `=a sin^(-1) 1`
`(3pi)/2` `=a xx pi/2`
`a` `= 3`
`:.\ y` `= 3 sin ^(-1)\ x/2`

 
`=>  C`