Graphing Sine and CosineDate: 07/07/2000 at 13:56:36 From: Bernadette Subject: Graphing sine and cosine I just don't understand how my teacher gets the points that he uses on the graph. I have tried to do the same thing he does over and over again, but it doesn't work. Please help me. Date: 07/07/2000 at 14:34:56 From: Doctor Jaffee Subject: Re: Graphing sine and cosine Hi Bernadette, I assume that you are talking about sketching the graph of a sinusoid; that is, an equation in one of the following forms: 1. y = C + AsinB(x - D) 2. y = C + AcosB(x - D) Here is how I would draw the graph. First, draw a dotted horizontal line C units above (or below if C is negative) the x-axis. This dotted line is the transverse axis. Half of the graph will be above the dotted line and half will be below. If D is positive, go D units to the right of the origin and, if you are drawing a type 1 equation (the one with the sine), go up to the transverse axis and put a dot. This will be the first point of the cycle. If D is negative, go to the left. If your equation is type 2, go D units to the left or right just as I suggested for type 1. Then if A is positive, put the dot A units above the transverse axis. If A is negative, the point will be below the transverse axis. Now, if you are doing a type 1 graph and x is in degrees, then the end of the cycle will be on the transverse axis, 360/B degrees to the right of the first point of the cycle. Halfway between these two points on the transverse axis will be the midway point of the cycle. If the equation is in radians, then the last point will be 2*pi/B units to the right of the first point. Halfway between the first point of the cycle and the midway point of the cycle, draw a point A units above (or below, if A is negative) the transverse axis. Halfway between the midway point and the end of the cycle, draw a point A units below (or above, if A is negative) the transverse axis. By now you should have 5 points. If you draw a smooth curve connecting them, you will have one cycle of the sinusoid. If you are graphing a type 2 sinusoid, then the first and last points of the cycle will be A units above the transverse axis and the midway point will be A units below the axis. Of course, if A is negative, just the opposite will happen. The points 1/4 and 3/4 of the way through the cycle will be on the transverse axis. I hope this explanation helps. Try a few examples and see what happens. If you are having difficulties or if some of my explanation was unclear, write back and I'll try to help you some more. - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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