Graphing (Trigonometric Functions)

Michigan State University - Diagnostic Exam

6.20

The sketch below is the graph of which of the following functions?

a) $( ) y = sin π-x + 1 2$ b) $y = cos x + 1$ c) $( ) y = cos π-x + 1 2$

d) $( ) y = sin π-x + 1 2$ e) $y = sin2πx + 1$

Solution:

The periodic function shown has an amplitude of $2 +2-0$ , a period of 5 - 1 and a “phase shift” of 0 (if we model this function using a sine wave). It follows that the function is given by

( 2π ) y = 1 ⋅ sin ---x + 1 ( )4 = sin π-x + 1 2

Diagnostic:

If you miss this question please review graphing trigonometric functions.

Also, see 3.10: Graphing (Geometric Transformations) .

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July 15, 2008