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Trigonometry: Graphs

Problems

Horizontal and Vertical Shifts

Vertical and Horizontal Stretches

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) or y = sin(x + 2k ) , where k is an integer.

Problem : State a formula for the following graph.

y = sin(x + 2) + 1 or y = cos(x - 2k ) + 1 , where k is an integer.

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