Question

Given the equation y = 7 sec(6x– 30)

The period is:

The horizontal shift is:

Answer 1

The period is of
`(\pi)/(3)` units.

The horizontal shift is of 30 units to the left.

Explanation:

The secant function has the following general format:

`y = A\sec{(Bx + C)}`

A represents the vertical shift.

C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.

The period is
`P = (2\pi)/(B)`

In this question:

`y = 7\sec{6x - 30}`

So
`B = 6, C = -30`

Then
`P = (2\pi)/(6) = (\pi)/(3)`

The period is of
`(\pi)/(3)` units.

The horizontal shift is of 30 units to the left.