Wednesday, October 2, 2013

GRAPHING TRIG FUNCTIONS

This is a quick note to reinforce my position on graphing trigonometry functions by using charts to calculate your 5 significant points (especially for Hira's upcoming quiz).  Drawing actual graphs take hours, so I’ll skip that part today and just focus on creating the charts of values.

If you want to take shortcuts and just wing it -- good luck.  But if you are looking for an A, I STRONGLY recommend doing the chart of values and plotting the graph from the data.  Even if you make a little mistake on the graph itself, the teacher has the chart to witness that you actually know what you are doing.  I’ll take partial points over no points any day.

So here are the charts and what to do with them.
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Take any trig equation in the form

A (trig function) B ( X + C ) + D

Using the basic chart for the trig function named, multiply Y values by A and add D.  Divide X by B and subtract C.

Notice that adding D to Y uses the SAME SIGN as the equation, while subtracting C from X uses the OPPOSITE SIGN.  Remember my “Sandi Rule” -- any time you use a number that’s attached to a variable, CHANGE THE SIGN.

TIPS:

¶  Leave sufficient room in your chart to do the calculations.  Working with fractions, where you might have to find a common denominator, can spread out a lot.  Don’t skimp on your working space.

§  Notice that the COSECANT sits where the SINE DOESN'T and the SECANT sits where the COSINE DOESN'T.  ASYMPTOTES appear in the cosecant and secant where the sine and cosine are zero.
§§  The same does NOT hold for Tangent and its reciprocal Cotangent.

∆  Remember that B must be the coefficient of the binomial (X + C).  If you are given (3X + 9), don't forget to factor out the 3 from BOTH 3X and 9.

Using the charts, you can focus attention on the arithmetic to avoid calculation mistakes.  Then transferring the data to the coordinate plane allows you to concentrate on the visual aspects of the graph.  Make it pretty.  Use colors to draw your final graph.  Have fun!!  This is the artistic portion of math.