http://www.ck12.org Chapter 5. Trigonometric Functions
Solution: First draw the new sinusoidal axis for each graph. Then, draw a complete sine wave for each one. Re-
member to draw the five important points that separate each quadrant to get a clear sense of the graph. Right now
every cycle starts at 0 and ends at 2πbut this will not always be the case.
Example B
Identify the equation of the following transformed cosine graph.
Solution: Since there is no sinusoidal axis given, you must determine the vertical shift, stretch and reflection. The
peak occurs at(π, 3 )and the trough occurs at (0, -1) so the horizontal line directly between +3 and -1 isy=1. Since
the sinusoidal axis has been shifted up by one unitd=1. From this height, the graph goes two above and two below
which means that the amplitude is 2. Since this cosine graph starts its cycle at (0, -1) which is a lowest point, it is a
negative cosine. The function isf(x) =−2 cosx+1.
Example C
Graph the following function:f(x) =−sinx−1.
Solution: Identify the important information. Then draw the sinusoidal axis.
- a= 1