smc-977-30-tan

Trigonometry, 2ADV T3 EQ-Bank 5 MC

The period of the function `f(x) = tan((pix)/2)` is

`2`
`4`
`2pi`
`4pi`

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`A`

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`n= pi/2`

`text{Period} = pi/n = pi/(pi/2)=2`

`=> A`

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)

--- 6 WORK AREA LINES (style=lined) ---

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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 EQ-Bank 7 MC

The function with equation `f(x) = 4 tan (x/3)` has period

`(2pi)/3`
`6 pi`
`3`
`3 pi`

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`D`

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`text(Period) =pi/n= pi/(1/3)= 3 pi`

`=> D`

Trigonometry, 2ADV T3 EQ-Bank 6 MC

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

The equation of `f(x)` could be

`f (x) = tan (x)`
`f (x) = tan (x-pi/4)`
`f (x) = tan(2 (x-pi/4))`
`f (x) = tan(2 (x-pi/2))`

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`C`

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`text(Period) = pi/2`

`=>\ text(must be)\ C\ text(or)\ D`

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

`=> C`

Trigonometry, 2ADV T3 2016 HSC 6 MC

What is the period of the function `f(x) = tan (3x)?`

`pi/3`
`(2 pi)/3`
`3 pi`
`6 pi`

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`A`

Show Worked Solution

♦ Mean mark 42%.

`text(Period)`	`= pi/n`
	`= pi/3`

`=> A`