**Problem : **
The graphs of which pairs of trigonometric
functions can be replaced by its
partner with either a horizontal or a vertical shift?

Sine and
cosine, and
secant and
cosecant are pairs in which each
partner is different from the other only as a result of a horizontal shift.

**Problem : **
What would happen to the sine graph if the equation were changed to this:
*y* = sin(*x*) - 3?

The graph would be shifted vertically down three units, but would otherwise be
the same.

**Problem : **
What would happen to the cosine graph if the equation were changed to this:
*y* = cos(*x* - )?

The graph would shift to the right by

units, and, incidentally,
overlap the sine graph.

**Problem : **
State a formula for the following graph.

*y* = cos(*x* + 2*kΠ*) or

*y* = sin(*x* + 2*k*), where

*k* is an integer.

**Problem : **
State a formula for the following graph.

*y* = sin(*x* + 2*kΠ*) + 1 or

*y* = cos(*x* - 2*k*) + 1, where

*k* is an integer.